{ "schema_version": "lib2-index-1.0", "status": "IN_REVIEW", "build_tag": "S371a", "round": "D1253", "built_at": "2026-09-26T22:53Z", "build_sha": "01d1a5873ede42f5b2c5f4fdcee3a4a74c09a14b99a0deea86a60ebd9c821033", "basis": "Rev33.1_S369 (PDF sha256 b64ddcd9e16a6dcd…)", "count": 357, "counts": { "by_class": { "CLAIM": 202, "COMPARATOR": 30, "RETIRED": 68, "OPEN": 19, "NOT_AN_ENTRY": 38 }, "blocked": 0, "candidates_covered": 208, "candidates_total": 208, "by_review_state": { "PUBLISHED": 280, "IN_REVIEW": 77 } }, "canonical": "/library-v2/library_v2.jsonl", "suite_text": "/papers/suite-text/", "entries": [ { "id": "LIB2-001", "entry_version": 11, "class": "CLAIM", "title": "Route-B admissible-gap classification", "statement": "For positive golden-field units a, b, c with abc = 1, the Route-B classification gives F = 16 only at the exponent multiset {1, 0, −1}; apart from the equal-spectrum case, every other admissible gap pair has F ≥ 41.", "scope": { "carrier": "Positive diagonal Jvac = diag(a, b, c)", "domain": "Appendix E, Route B; F is the gap functional defined in the proof of Theorem 2.", "group": null, "hypotheses": [ "a, b, c are positive units of Z[ϕ], with abc = 1.", "Write a = ϕ^n1, b = ϕ^n2, c = ϕ^n3 with n1 + n2 + n3 = 0; order n1 ≥ n2 ≥ n3.", "The nonnegative gaps p = n1 − n2 and q = n2 − n3 obey p + 2q ≡ 0 (mod 3)." ], "physical_target": null, "quantifier": "All admissible gap pairs in the printed arithmetic classification.", "real_form": "J3(Os)" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 165 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "analytic", "availability": "shipped" }, { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix E", "section": "§4, Theorem 2: admissible-gap case count", "pdf_page": 171, "quote": "(p, q) = (1, 1) — the triple {1, 0, −1} — gives F = 3 + 3 + 3 + 7 = 16; no other pair with p + q ≤ 2 is admissible (p + 2q ≡ 0 (mod 3) excludes (1, 0), (0, 1), (2, 0), (0, 2)); for p + q = 3 the admissible pairs are (3, 0) and (0, 3), each giving F = 3 + 18 + 2 + 18 = 41 (attained at {2, −1, −1}); and for p + q ≥ 4, Ap+q ≥ 47 gives F ≥ 3 + 47 + 2 + 2 = 54" }, "caution": "This gap classification does not select the golden-field hypothesis or the ordered physical Peirce frame, and it does not supply a physical vacuum-selection law.", "candidate_ids": [ "C2-111" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-020" }, { "type": "cited_by_section", "target": "E-C04.1.claims-used" }, { "type": "cited_by_section", "target": "E-C04.1.derivation" }, { "type": "cited_by_section", "target": "E-C04.1.prior-art" }, { "type": "cited_by_section", "target": "E-C04.1.sources-receipt" }, { "type": "rests_on_premise", "target": "PRM-024" } ], "url": "/library-v2/LIB2-001/", "content_sha256": "cb263cc9d60e7eefdc392d9a5e109dcfa3ee16aa24105056057b1226784566ac", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-002", "entry_version": 9, "class": "CLAIM", "title": "Physical atmospheric registration of the internal 7/16 mismatch", "statement": "The registration sin²θ₂₃ = 7/16 is a Loaded-correspondence: the chirality and octant torsors admit exactly two equivariant bijections, and the registered map chooses one by convention.", "scope": { "carrier": "Chirality torsor and atmospheric-octant torsor", "domain": "PMNS atmospheric mixing", "group": "Z2-equivariant registrations", "hypotheses": [ "The internal mismatch identity is recorded separately in G-360.", "The registered chirality-to-octant correspondence chooses one equivariant bijection by convention." ], "physical_target": "sin²θ₂₃ = 7/16, lower-octant registration", "quantifier": "The retained physical registration, not every equivariant identification.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "Loaded-correspondence", "scorecard_tier_word": null, "pdf_page": 59 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" }, { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Paper 3", "section": "§5.4, What survives, and it is not nothing", "pdf_page": 64, "quote": "A1566/D1244 finds that s501 does not uniquely register that mismatch to the physical lower atmospheric octant: the chirality torsor and the octant torsor admit exactly two equivariant bijections and s501 chooses one by convention." }, "caution": "This registration does not derive the physical atmospheric octant. Excluding the loaded physical target does not by itself refute the internal mismatch identity unless the readout attachment is first derived.", "candidate_ids": [ "C2-005", "C2-059" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "depends_on", "target": "LIB2-356" }, { "type": "compares_with", "target": "SL-25" }, { "type": "rests_on_premise", "target": "PRM-012" } ], "url": "/library-v2/LIB2-002/", "content_sha256": "b8d4b0e005af4b17daf506288ac1f7d6f67ea47d76ab0e705904126010a5f9bf", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-003", "entry_version": 7, "class": "COMPARATOR", "title": "SL-25: NuFIT 6.1 lower-octant atmospheric comparator", "statement": "The ledger’s NuFIT normal-hierarchy, lower-octant comparator for sin²θ₂₃ is 0.470 with asymmetric errors +0.017 and −0.014.", "scope": { "carrier": null, "domain": "NuFIT 6.1 NH global fit, with SK atmospheric data, lower octant", "group": null, "hypotheses": [], "physical_target": "sin²θ₂₃", "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 325 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "COMPARATOR", "evidence_status": [ { "kind": "external", "availability": "shipped" } ], "primary_source": { "component": "Appendix X", "section": "Honest precision summary: Atmospheric angle bullet", "pdf_page": 345, "quote": "NuFIT 6.1 NH (w/SK) global best fit 0.470+0.017 −0.014" }, "caution": null, "candidate_ids": [ "C2-203" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-003/", "content_sha256": "65fd240127992ad0c0661cf704b4070eceec4b86599979ac9835e3385cfd8800", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-004", "entry_version": 9, "class": "RETIRED", "title": "Retired house atmospheric assertion: sin²θ₂₃ = 4/7", "statement": "The house entry presented an atmospheric squared-sine value as derived; its supplied source header now flags that assertion as superseded.", "scope": { "carrier": null, "domain": "Historical PMNS atmospheric assertion", "group": null, "hypotheses": [], "physical_target": "sin²θ₂₃", "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 3", "section": "§5.4, Current replacement attachment", "pdf_page": 64, "quote": "The current physical θ23 row is therefore Loaded-correspondence; the number and the internal theorem do not move." }, "caution": null, "candidate_ids": [ "C2-169" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-004/", "content_sha256": "f4adb12a740c67bca6f6bde69250b256a7496864d26a50632d6814de66c2b9d4", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-005", "entry_version": 7, "class": "OPEN", "title": "Joint basepoint and microscopic observation-map construction", "statement": "Can a theory-selected basepoint subgroup and a microscopic support-restoring observation map be constructed jointly, as required before the physical spectral-pair/output gate may be opened?", "scope": { "carrier": "Unpointed 27 and the microscopic mass/generation readout", "domain": "Appendix T §15.5–15.6; not the already constructed OMOS record quotient", "group": "A subgroup Hbp of E6(6), not yet selected", "hypotheses": [ "Register the subgroup before naming any vector or frame.", "Its action must have a single non-null fixed line; cubic normalization selects a point subject to trivial residual-normalizer action." ], "physical_target": "Microscopic spectral-pair/output gate", "quantifier": "A joint construction meeting the printed source requirements.", "real_form": "E6(6)" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 317 }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "OPEN", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix T", "section": "§15.5, Intrinsic-basepoint placeholder", "pdf_page": 335, "quote": "A future intrinsic selector must register, before naming any vector or frame, a subgroup Hbp ⊂ E6(6) whose action on the unpointed 27 has a single non-null fixed line. The cubic normalization N (x0 ) = 1 would then select one real point on that line, subject to the residual normalizer acting trivially." }, "caution": "The constructed OMOS record quotient is not the missing microscopic mass/generation observation map; entering its output gate is not asserted to derive a physical mixing matrix.", "candidate_ids": [ "C2-067", "C2-088", "C2-097", "C2-133" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-174" }, { "type": "related_to", "target": "LIB2-175" }, { "type": "related_to", "target": "LIB2-178" }, { "type": "related_to", "target": "LIB2-186" } ], "url": "/library-v2/LIB2-005/", "content_sha256": "d411996595c7f6e928b57e141aec0a7cfa13dd33ab79685f94f1c361736dc91e", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-006", "entry_version": 8, "class": "CLAIM", "title": "The registered symplectic exceptional substrate", "statement": "The registered split E7(7) substrate acts on the real 56 through 133 generators, preserves the symplectic form, and has a quartic-invariant stabilizer of dimension 133.", "scope": { "carrier": "Real V56 and its registered generator action", "domain": "Appendix F §1: ambient substrate, not the embedding-tensor or potential layers.", "group": "E7(7)", "hypotheses": [ "The project's e7_substrate construction and V1–V6 conventions are fixed." ], "physical_target": null, "quantifier": "The registered carrier and source conventions.", "real_form": "E7(7)" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 174 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix F", "section": "§1, Scope and provenance: V1–V6", "pdf_page": 180, "quote": "the certified ambient E7(7) substrate (V1–V6: 133 generators on the 56, signature +7, symplectic, quartic-invariant stabilizer of dimension exactly 133)" }, "caution": "This carrier realization does not select a compact Standard-Model frame, a gauging or a physical observable.", "candidate_ids": [ "C2-035" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "cited_by_section", "target": "E-C03.1.claims-used" }, { "type": "cited_by_section", "target": "E-C03.1.derivation" }, { "type": "cited_by_section", "target": "E-C03.1.prior-art" }, { "type": "cited_by_section", "target": "E-C03.1.sources-receipt" } ], "url": "/library-v2/LIB2-006/", "content_sha256": "65ff7b43195e41d7a67d71a998315b3e104f3152e5ec45cd8933231f3a77b1e1", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-007", "entry_version": 7, "class": "CLAIM", "title": "The identity-anchored complementary scalar sector", "statement": "The missing 16-scalar sector is identified as the identity-anchored Jordan complement 42 ⊖ 26 inside the maximal-supergravity coset.", "scope": { "carrier": "Identity-anchored scalar complement inside the maximal-supergravity coset", "domain": "The complement identification printed in Paper 4, not a new field-level extraction.", "group": "E7(7)", "hypotheses": [ "The Albert identity anchors the Jordan-visible scalar sector in the registered substrate." ], "physical_target": null, "quantifier": "The registered carrier and source conventions.", "real_form": "E7(7)/SU(8)" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 69 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Paper 4", "section": "§4.2, Ghost-free reading: identity-anchored complement", "pdf_page": 73, "quote": "the missing 16 is the identity-anchored Jordan complement 42 ⊖ 26 inside the maximal-SUGRA coset, pinned on the certified E7(7) substrate." }, "caution": "The complement identification is not a consistent truncation to the Jordan-visible sector and does not establish the unprinted named-projector certificate.", "candidate_ids": [ "C2-036" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "cited_by_section", "target": "E-C03.2.claims-used" }, { "type": "cited_by_section", "target": "E-C03.2.computations" }, { "type": "cited_by_section", "target": "E-C03.2.derivation" }, { "type": "cited_by_section", "target": "E-C03.2.prior-art" }, { "type": "cited_by_section", "target": "E-C03.2.sources-receipt" } ], "url": "/library-v2/LIB2-007/", "content_sha256": "418e1005ab87dad7517868b84db049068bc4f01a7ecc1c727eda84f7464601b9", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-008", "entry_version": 8, "class": "CLAIM", "title": "The Jordan-visible scalar plane fails the Lie-triple criterion", "statement": "The Jordan-visible 54-plane is not a Lie-triple system: its triple brackets have nonzero projection onto the missing-16 sector.", "scope": { "carrier": "Jordan-visible tangent 54-plane and complementary 16-plane", "domain": "Scalar sigma-model Lie-triple test; the reported enumeration is exhaustive in the leading block.", "group": "E7(7)", "hypotheses": [ "The registered Jordan-visible plane and the ambient symmetric-space brackets are fixed." ], "physical_target": null, "quantifier": "The named plane, not all possible scalar subspaces.", "real_form": "E7(7)/SU(8)" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 181 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix F", "section": "§5.3, Jordan-54 Lie-triple test", "pdf_page": 187, "quote": "The Jordan-54 is NOT a Lie-triple system: the projection of [[54, 54], 54] onto the missing-16 has order-one components" }, "caution": "This is a scalar sigma-model obstruction for the named plane; vector-sector and other truncation claims do not follow.", "candidate_ids": [ "C2-033" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-007" }, { "type": "cited_by_section", "target": "E-C03.2.claims-used" }, { "type": "cited_by_section", "target": "E-C03.2.prior-art" }, { "type": "cited_by_section", "target": "E-C03.2.sources-receipt" } ], "url": "/library-v2/LIB2-008/", "content_sha256": "5ad50e57739ca64caf3860d4f637aa95fd4a870a77c152917a5948d5c3a504c2", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-009", "entry_version": 7, "class": "CLAIM", "title": "The complementary tangent plane closes as a Lie-triple system", "statement": "The registered missing-16 tangent plane is a Lie-triple system at the basepoint of E7(7)/SU(8), as reported to machine precision.", "scope": { "carrier": "Registered missing-16 tangent plane", "domain": "The local tangent-plane computation in Appendix F §5.3 and Paper 4 §4.2.", "group": "E7(7)", "hypotheses": [ "The basepoint, tangent plane and registered ambient brackets are fixed." ], "physical_target": null, "quantifier": "The named tangent plane at the basepoint.", "real_form": "E7(7)/SU(8)" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 181 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix F", "section": "§5.3, Missing-16 Lie-triple test", "pdf_page": 187, "quote": "The missing-16 IS a Lie-triple system, to machine precision (4.9 × 10−15 over all 1,920 triples)." }, "caution": "Local Lie-triple closure does not establish the global embedded quotient or a vector-coupled physical truncation.", "candidate_ids": [ "C2-033" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-007" }, { "type": "cited_by_section", "target": "E-C03.2.claims-used" }, { "type": "cited_by_section", "target": "E-C03.2.prior-art" }, { "type": "cited_by_section", "target": "E-C03.2.sources-receipt" } ], "url": "/library-v2/LIB2-009/", "content_sha256": "474ec0cd2c65ba2bd6d0af39b7cd5e82bc077c49a164b5b33c19e7833ce2304f", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-010", "entry_version": 10, "class": "CLAIM", "title": "The algebra generated by the complementary tangent plane", "statement": "The missing-16 plane generates a 28-dimensional algebra identified with so(4,4), whose compact part is so(4) ⊕ so(4) of dimension 12.", "scope": { "carrier": "g′ = [16,16] ⊕ 16 generated by the registered complementary plane", "domain": "Generated Lie-algebra identification; its associated symmetric-space identification is local.", "group": "SO(4,4)", "hypotheses": [ "The registered plane, brackets and source normalization are used." ], "physical_target": null, "quantifier": "The algebra generated by this plane.", "real_form": "so(4,4) with compact part so(4) ⊕ so(4)" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 181 }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix F", "section": "§5.3, Generated-algebra identification", "pdf_page": 187, "quote": "Cartan character +4 — a tuple that by itself does not distinguish so(4, 4) from g2(2) ⊕ g2(2)" }, "caution": "This local Lie-algebra identification does not prove geodesic completeness, embedding closedness or a global quotient identification.", "candidate_ids": [ "C2-033" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-009" }, { "type": "cited_by_section", "target": "E-C03.2.claims-used" }, { "type": "cited_by_section", "target": "E-C03.2.computations" }, { "type": "cited_by_section", "target": "E-C03.2.derivation" }, { "type": "cited_by_section", "target": "E-C03.2.prior-art" }, { "type": "cited_by_section", "target": "E-C03.2.sources-receipt" } ], "url": "/library-v2/LIB2-010/", "content_sha256": "88ab4c09fac97ff248ef3522e75e772160c7c4dd5b39112ff6b64088e7f00dd7", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-011", "entry_version": 7, "class": "CLAIM", "title": "The cubic Jordan slice is a Lagrangian boundary of the FTS", "statement": "The slice LJ = Re− ⊕ J+2 carrying the golden ladder is a 28-dimensional Lagrangian subspace of the real FTS 56.", "scope": { "carrier": "LJ = Re− ⊕ J+2 in the Freudenthal carrier", "domain": "The kinematic Jordan-boundary statement in Appendix X.", "group": "E7(7)", "hypotheses": [ "The registered FTS symplectic form and the named mass-coordinate slice are fixed." ], "physical_target": null, "quantifier": "The named real slice and symplectic pairing.", "real_form": "Split J3(Os), E7(7)" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 348 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix X", "section": "P0-1 audit, The result: definition of LJ", "pdf_page": 369, "quote": "Writing LJ = Re− ⊕ J+2 for the slice carrying the golden ladder:" }, "caution": "The symplectic form contributes kinematics, not a mass-sector Hamiltonian or dynamics selector; the conjugate-section attachment remains open.", "candidate_ids": [ "C2-032" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "cited_by_section", "target": "E-C03.1.claims-used" }, { "type": "cited_by_section", "target": "E-C03.1.derivation" }, { "type": "cited_by_section", "target": "E-C03.1.prior-art" }, { "type": "cited_by_section", "target": "E-C03.1.sources-receipt" } ], "url": "/library-v2/LIB2-011/", "content_sha256": "fda5dab99db77b8484e7c040bff52432dee31af48504a4a40480ec6c22361c13", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-012", "entry_version": 7, "class": "CLAIM", "title": "The Albert-to-shell polarized-cubic solder", "statement": "The rank-27 solder B from J3(Os) to the grade −2 shell preserves the full polarized cubic: Cshell(Bx,By,Bz) = Npol(x,y,z).", "scope": { "carrier": "J3(Os) and the grade −2 shell V−2", "domain": "Tensor equivalence of the Albert and shell carriers.", "group": "E7(7)", "hypotheses": [ "The registered solder B and the source and shell polarized cubics are fixed." ], "physical_target": null, "quantifier": "The complete polarized-cubic identity for the named solder.", "real_form": "Split Albert algebra inside the real E7(7) carrier" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 314 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix T", "section": "§15.1, The solder and transported pointing", "pdf_page": 332, "quote": "The carrier arc begins with the exact rank-27 solder" }, "caution": "Tensor equivalence does not make the unpointed shell select the transported unit or an intrinsic basepoint.", "candidate_ids": [ "C2-089" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-005" }, { "type": "cited_by_section", "target": "E-C03.1.claims-used" }, { "type": "cited_by_section", "target": "E-C03.1.derivation" }, { "type": "cited_by_section", "target": "E-C03.1.prior-art" }, { "type": "cited_by_section", "target": "E-C03.1.sources-receipt" } ], "url": "/library-v2/LIB2-012/", "content_sha256": "c52bca63e8261c9df5861bb1cd9832aa7e4f7b65550dea0d65d101df3af15b26", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-013", "entry_version": 7, "class": "CLAIM", "title": "Local positive paired-shell polarization at the transported point", "statement": "At the transported point, the trace-dual polarization gives a positive three-complex-dimensional paired-shell space up to the shell-exchange torsor.", "scope": { "carrier": "Trace-dual paired-shell space at the transported point", "domain": "Appendix T's dated local amendment to face 3.", "group": null, "hypotheses": [ "The transported point and trace-dual polarization are supplied.", "The shell-exchange torsor is not resolved." ], "physical_target": null, "quantifier": "Local existence at the transported point.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 315 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix T", "section": "§15.1, Dated amendments to Table 1: face 3", "pdf_page": 333, "quote": "Face 3 closes locally at the transported point up to the shell-exchange torsor: the trace-dual polarization gives a positive three-complex-dimensional paired shell space, while intrinsic unpointed selection remains open [A1557]." }, "caution": "This local polarization does not select an intrinsic unpointed structure, a torsor side or the microscopic mass/generation readout.", "candidate_ids": [ "C2-089" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-012" }, { "type": "related_to", "target": "LIB2-005" }, { "type": "cited_by_section", "target": "E-C03.1.claims-used" }, { "type": "cited_by_section", "target": "E-C03.1.derivation" }, { "type": "cited_by_section", "target": "E-C03.1.prior-art" }, { "type": "cited_by_section", "target": "E-C03.1.sources-receipt" } ], "url": "/library-v2/LIB2-013/", "content_sha256": "c2e7eb5130dd7155f61bb4e33b8dd10b0dded030278b857753d7618f21656c23", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-014", "entry_version": 7, "class": "CLAIM", "title": "The active braid carrier consists of twelve Clifford-module copies", "statement": "The active carrier of the frozen braid representation is a Cl(2,1) module in exactly 12 copies.", "scope": { "carrier": "Active carrier of the frozen braid representation", "domain": "The active Clifford-module structure, separate from the clock/selector coefficient identity.", "group": "so(2,1)", "hypotheses": [ "The frozen carrier and braid/trace grammar are fixed." ], "physical_target": null, "quantifier": "The active sector, not the whole carrier as a nontrivial module.", "real_form": "Real Cl(2,1) module" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 169 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix E", "section": "§7, The dark attachment: provenance upgrade", "pdf_page": 175, "quote": "the active carrier is a Cl(2, 1) module in exactly 12 copies" }, "caution": "The Clifford-module count does not select measured time, a physical energy scale or an occupation rule.", "candidate_ids": [ "C2-103" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "cited_by_section", "target": "E-C05.2.claims-used" }, { "type": "cited_by_section", "target": "E-C05.2.definitions-conventions" }, { "type": "cited_by_section", "target": "E-C05.2.derivation" }, { "type": "cited_by_section", "target": "E-C05.2.prior-art" }, { "type": "cited_by_section", "target": "E-C05.2.sources-receipt" } ], "url": "/library-v2/LIB2-014/", "content_sha256": "555c9fc7454cdafc302eef65cde688ccb1b211d58d0d47779c1da8951bf0e7c8", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-015", "entry_version": 8, "class": "CLAIM", "title": "The golden braid-word square root on the frozen carrier", "statement": "In the frozen 56-frame, the braid hyperbolic word Wh has an exact symplectic unimodular square root Hϕ with Hϕ² = Wh and eigenvalues φ⁻¹, 1 and φ of multiplicities 12, 32 and 12.", "scope": { "carrier": "Frozen real 56-frame and its braid hyperbolic word", "domain": "Appendix H §11, the algebraic square-root construction.", "group": "Sp(V56)", "hypotheses": [ "Wh, P, Q and the Clifford generators are those of the frozen representation.", "The source sets A = Wh − Q with A² − 3A + P = 0." ], "physical_target": null, "quantifier": "The specified braid word in the frozen frame.", "real_form": "Real symplectic carrier" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 198 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix H", "section": "§11, Theorem 11.1: frozen-word setup", "pdf_page": 205, "quote": "Within the frozen 56-frame let Wh = Q + 32 P + 32 γ1 − γ2 be the braid hyperbolic word and set A = Wh − Q, so that A2 − 3A + P = 0." }, "caution": "This finite spectral construction does not attach the braid word to a physical mass, an absolute energy scale or an occupied winding level.", "candidate_ids": [ "C2-104" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-014" }, { "type": "cited_by_section", "target": "E-C05.2.claims-used" }, { "type": "cited_by_section", "target": "E-C05.2.prior-art" }, { "type": "cited_by_section", "target": "E-C05.2.sources-receipt" } ], "url": "/library-v2/LIB2-015/", "content_sha256": "db97b610554c7278b97a6640cd097c96b114a1b5b40b2924592c8a33d85ce8aa", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-016", "entry_version": 8, "class": "CLAIM", "title": "The physical-vector ten and selector ten are isomorphic modules", "statement": "Inside V56, the so(5,5) physical-vector ten is isomorphic to the selector ten as a Kdyn module, with Casimir 1/6.", "scope": { "carrier": "Physical/vector ten and selector ten in V56", "domain": "Appendix X's three-ten carrier fence.", "group": "Kdyn", "hypotheses": [ "The two named carriers and the registered Kdyn action and normalization are fixed." ], "physical_target": null, "quantifier": "These two modules in the frozen carrier.", "real_form": "so(5,5) vector within the real split-exceptional carrier" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 349 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix X", "section": "Carrier fence beside clause 27: three tens", "pdf_page": 371, "quote": "The physical/vector ten (the so(5, 5) vector inside V56 , Kdyn -Casimir 1/6) is isomorphic to the selector ten (two-host certified; kernel s1067)" }, "caution": "This module isomorphism does not identify either ten with the distinct boundary-adjoint module.", "candidate_ids": [ "C2-109" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-016/", "content_sha256": "ca4cc4281346dfadf496b252db2eb2d2e71ccfc7d4aacd3bada2aa836e053a16", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-017", "entry_version": 11, "class": "CLAIM", "title": "The boundary and selector tens have no equivariant linear intertwiner", "statement": "The boundary-adjoint ten and selector ten are inequivalent Kdyn modules: the boundary-adjoint ten has Casimir 1/4 and the selector ten has Casimir 1/6, and HomKdyn = 0.", "scope": { "carrier": "Boundary-adjoint ten and selector Π10 sector", "domain": "Linear Kdyn-equivariant maps between the named modules.", "group": "Kdyn", "hypotheses": [ "The boundary tangent module, selector sector and registered Casimir normalization are fixed." ], "physical_target": null, "quantifier": "The boundary and selector modules in the declared class.", "real_form": "Registered real Kdyn modules" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 296 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix S", "section": "§9.2, Theorem 9.2: declared-class negative", "pdf_page": 313, "quote": "The boundary ten (the tangent module of the priced ten-continuous boundary object of Appendix E’s closure section) and the selector ten (the Π10 sector) are inequivalent Kdyn -modules: their Casimirs are 14 I and 16 I exactly, so HomKdyn = 0 by Schur" }, "caution": "The linear-intertwiner obstruction does not exclude the separately counted nonlinear or symmetry-breaking bridge classes.", "candidate_ids": [ "C2-109" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-016" } ], "url": "/library-v2/LIB2-017/", "content_sha256": "5379d27a50eaecdb5f3ced5559197c543552840222775372d0d082eddacc107b", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-018", "entry_version": 9, "class": "CLAIM", "title": "DET-7 is a structural postulate in the algebraic selector", "statement": "In Appendix E's algebraic selector, det Gram(Jvac,Jvac#) = 7 is imposed as the DET-7 structural postulate, not derived as a necessity.", "scope": { "carrier": "Positive diagonal Jordan element and its adjoint", "domain": "The premise role of DET-7 in the algebraic selector, not its evaluation on an already selected spectrum.", "group": null, "hypotheses": [ "Unit Jordan determinant is the normalization.", "Route A also assumes inversion symmetry; Route B instead restricts to positive golden-field units." ], "physical_target": null, "quantifier": "The declared class only.", "real_form": "J3(Os)" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 164 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix E", "section": "§3, Remark 2: status of H2", "pdf_page": 171, "quote": "DET-7 enters this appendix as a structural postulate, not a derived necessity; the result is therefore a conditional selector theorem." }, "caution": "This postulate does not establish its own first-principles necessity or the physical attachment of the resulting invariant.", "candidate_ids": [ "C2-003" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "cited_by_section", "target": "E-C04.1.claims-used" }, { "type": "cited_by_section", "target": "E-C04.1.prior-art" }, { "type": "cited_by_section", "target": "E-C04.1.sources-receipt" } ], "url": "/library-v2/LIB2-018/", "content_sha256": "ea6b5b300fbaa7acdd1917b9a314adc328ca0604f72bca710e3c57656d1ff2a0", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-019", "entry_version": 7, "class": "CLAIM", "title": "Route A selects the positive golden spectrum under its stated hypotheses", "statement": "A positive real diagonal Jvac satisfying unit determinant, inversion symmetry and DET-7 has spectrum {ϕ,1,ϕ⁻¹}, unique up to permutation.", "scope": { "carrier": "Positive real diagonal Jvac in J3(Os)", "domain": "Appendix E Route A; no number-field restriction is used.", "group": null, "hypotheses": [ "H0: Det(Jvac) = 1.", "H1: Jvac is isospectral to its Jordan adjoint; at unit determinant this is inversion symmetry.", "H2: det Gram(Jvac,Jvac#) = 7." ], "physical_target": null, "quantifier": "Every positive real diagonal element satisfying H0–H2.", "real_form": "J3(Os)" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 164 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "analytic", "availability": "shipped" } ], "primary_source": { "component": "Appendix E", "section": "§3, Theorem 1: symmetry-form selector", "pdf_page": 170, "quote": "A real positive diagonal Jvac ∈ J3 (Os ) satisfying (H0)–(H2) is unique up to permutation:" }, "caution": "The theorem selects a spectral orbit only; it neither derives DET-7 nor selects an ordered physical Peirce frame.", "candidate_ids": [ "C2-102" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "uses_input", "target": "LIB2-018" }, { "type": "rests_on_premise", "target": "PRM-013" }, { "type": "rests_on_premise", "target": "PRM-023" }, { "type": "cited_by_section", "target": "E-C04.1.claims-used" }, { "type": "cited_by_section", "target": "E-C04.1.prior-art" }, { "type": "cited_by_section", "target": "E-C04.1.sources-receipt" } ], "url": "/library-v2/LIB2-019/", "content_sha256": "45087f33b267c3a0bf1f5263a6eb47481f9a1a405f3e2d8656d3eeb52b15a560", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-020", "entry_version": 9, "class": "CLAIM", "title": "Route B selects the positive golden-unit triple under DET-7", "statement": "For positive algebraic integers a,b,c in Q(√5) with abc = 1 and DET-7, Jvac = diag(a,b,c) has spectrum {ϕ,1,ϕ⁻¹} up to permutation.", "scope": { "carrier": "Positive diagonal Jvac = diag(a,b,c)", "domain": "Appendix E Route B with the replaced admissible-gap proof.", "group": null, "hypotheses": [ "a,b,c are positive algebraic integers in Q(√5).", "abc = 1, so the entries are units of Z[ϕ].", "H2: det Gram(Jvac,Jvac#) = 7." ], "physical_target": null, "quantifier": "Every triple satisfying the printed arithmetic hypotheses.", "real_form": "J3(Os)" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 165 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "analytic", "availability": "shipped" } ], "primary_source": { "component": "Appendix E", "section": "§4, Theorem 2: arithmetic selector", "pdf_page": 171, "quote": "Let Jvac = diag(a, b, c) with a, b, c > 0 algebraic integers in Q( 5) and abc = 1. Then (H2) forces Jvac = diag(ϕ, 1, ϕ−1 ) up to permuta- tion." }, "caution": "The arithmetic hypothesis and DET-7 remain premises; this result is not a derivation of the ordered physical frame or of an action.", "candidate_ids": [ "C2-102" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "uses_input", "target": "LIB2-018" }, { "type": "rests_on_premise", "target": "PRM-013" }, { "type": "rests_on_premise", "target": "PRM-024" }, { "type": "cited_by_section", "target": "E-C04.1.claims-used" }, { "type": "cited_by_section", "target": "E-C04.1.derivation" }, { "type": "cited_by_section", "target": "E-C04.1.prior-art" }, { "type": "cited_by_section", "target": "E-C04.1.sources-receipt" } ], "url": "/library-v2/LIB2-020/", "content_sha256": "51dc78f16e2db545cbbde6fa79ec04f645ed89f162006264ab1bd6c608be7915", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-021", "entry_version": 11, "class": "CLAIM", "title": "The finite loaded-profile parent action has its stated stable minimum", "statement": "Within the frozen split-real 56-frame and declared finite/internal loaded-profile class, Vtotal attains its stated global minimum at M* = I and the displayed source-aligned pair (j*,q*), with combined Hessian positive for every ρ,u0,κd > 0 on the directions transverse to the exact projective soft ray [W0] at zero inserted dark amplitude, along which it vanishes.", "scope": { "carrier": "Finite/internal loaded-profile selector in the frozen real V56", "domain": "Configuration-space minimum and stability, not the velocity Hessian used in the Legendre step.", "group": null, "hypotheses": [ "The loaded boundary datum and assembled selector action are supplied.", "ρ,u0,κd are positive; no numerical values are fixed." ], "physical_target": null, "quantifier": "All positive parameters in the declared class.", "real_form": "Split-real 56-frame" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 170 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix E", "section": "§7, Closure declaration: minimum and Hessian", "pdf_page": 177, "quote": "the selector parent action Vtotal has its global minimum at (j ∗ , q ∗ = 32 j ∗ , M ∗ = I) with combined Hessian positive for all ρ, u0 , κd > 0 on the directions transverse to [W0 ], the exact projective soft ray at zero inserted dark amplitude, along which it vanishes (scope stated Rev32.9, A1632)." }, "caution": "This finite configuration-space closure is not a continuum Hamiltonian or an interacting pole/LSZ construction.", "candidate_ids": [ "C2-105" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "cited_by_section", "target": "E-C04.2.claims-used" }, { "type": "cited_by_section", "target": "E-C04.2.derivation" }, { "type": "cited_by_section", "target": "E-C04.2.prior-art" }, { "type": "cited_by_section", "target": "E-C04.2.sources-receipt" }, { "type": "rests_on_premise", "target": "PRM-010" } ], "url": "/library-v2/LIB2-021/", "content_sha256": "ded57726ab8a0d82c2cb7e4449fb531e4f1726d205f11f1630594cf9e382dff9", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-022", "entry_version": 8, "class": "CLAIM", "title": "The finite selector closure retains the stated boundary and coupling price", "statement": "The incremental price of the declared finite selector closure is 10 + 1 continuous: one ten-continuous boundary object, represented in three equivalent ways, and one positive dark coupling; discrete lifts remain degeneracies rather than consumed data.", "scope": { "carrier": "Boundary datum [j] ⇔ L∂ ⇔ E* and dark coupling κd", "domain": "Incremental price of this selector closure, not a total for the whole programme.", "group": null, "hypotheses": [ "The frozen-frame finite/internal loaded-profile class is fixed.", "The boundary equivalence concerns the three registered faces of one datum." ], "physical_target": null, "quantifier": "The declared class only.", "real_form": "Split-real 56-frame" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 170 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix E", "section": "§7, Boundary datum: three faces", "pdf_page": 175, "quote": "The datum the action is conditional on is single: [j] ⇐⇒ L∂ ⇐⇒ E ∗ = span{iB j, ΩiB j} — three faces of one ten-continuous boundary object, priced once." }, "caution": "This incremental price neither derives the boundary datum nor supplies a programme-wide count of physically distinguishable inputs.", "candidate_ids": [ "C2-105" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-021" }, { "type": "cited_by_section", "target": "E-C04.2.claims-used" }, { "type": "cited_by_section", "target": "E-C04.2.derivation" }, { "type": "cited_by_section", "target": "E-C04.2.sources-receipt" } ], "url": "/library-v2/LIB2-022/", "content_sha256": "8f1d264322081cd7eb8e41cf3f6deede48dfc0cc40d5404992fdc5fea42b290c", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-023", "entry_version": 7, "class": "CLAIM", "title": "The grammar detector selects the dark ray", "statement": "The frozen braid/trace grammar's detector quadratic form has the unique top eigenspace R W0, identifying the dark axis within the declared selector construction.", "scope": { "carrier": "Detector quadratic form on the registered p-sector", "domain": "The dark-axis selection statement of Appendix E §7, distinct from boundary-source selection.", "group": "Kdyn", "hypotheses": [ "The frozen braid/trace grammar and its detector quadratic form are fixed." ], "physical_target": null, "quantifier": "The declared class only.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 169 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix E", "section": "§7, Dark attachment: detector eigenspace", "pdf_page": 176, "quote": "The crown is prefrozen: the grammar’s own detector quadratic form on the 70-dimensional p-sector has spectrum 01 ⊕ (5/3)10 ⊕ 226 ⊕ (5/2)32 ⊕ (9/2)1 (house-recomputed exact) with a unique top eigenspace, frozen pre-target and shown post-freeze to be exactly RW0 (overlap 1.000000000000)." }, "caution": "Selecting this dark ray does not select the distinct loaded boundary source ray or the nonlinear action shape.", "candidate_ids": [ "C2-105" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-021" }, { "type": "related_to", "target": "LIB2-022" }, { "type": "cited_by_section", "target": "E-C04.2.claims-used" }, { "type": "cited_by_section", "target": "E-C04.2.derivation" }, { "type": "cited_by_section", "target": "E-C04.2.sources-receipt" } ], "url": "/library-v2/LIB2-023/", "content_sha256": "d0f0114182176c1b920e7a0f6a08ee4205646106719202fdbbf2c49c2ff0bcb6", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-024", "entry_version": 7, "class": "CLAIM", "title": "The selector law and clock commutator share one structure constant", "statement": "On the frozen carrier, the selector-law coefficient equals the clock commutator coefficient: κlaw = κclock, the same structure constant read as an eigenvalue difference and as a commutator coefficient.", "scope": { "carrier": "Frozen braid/trace carrier and its clock generators", "domain": "Equality within the finite frozen representation, not a measured clock-frequency identification.", "group": null, "hypotheses": [ "The registered active Clifford-module structure and generator normalization are fixed." ], "physical_target": null, "quantifier": "The declared class only.", "real_form": "Real 56-frame" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 169 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix E", "section": "§7, Dark attachment: coefficient identity", "pdf_page": 175, "quote": "κlaw = κclock is a theorem — one structure constant appearing simultaneously as an eigenvalue difference and as the commutator coefficient" }, "caution": "The shared internal coefficient does not derive external time, an absolute frequency or a physical mass scale.", "candidate_ids": [ "C2-103" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "depends_on", "target": "LIB2-014" }, { "type": "cited_by_section", "target": "E-C04.2.claims-used" }, { "type": "cited_by_section", "target": "E-C04.2.derivation" }, { "type": "cited_by_section", "target": "E-C04.2.sources-receipt" } ], "url": "/library-v2/LIB2-024/", "content_sha256": "63c62276261139a8ec00d535f1ddba0665afe4f6691ca30183e4d0924cc5e52e", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-025", "entry_version": 10, "class": "CLAIM", "title": "The loaded-plane defect algebra determines the selector eigenspaces", "statement": "The loaded plane PB forces the 26 ⊕ 10 interior split, and its symplectic transport defect, with the commuting joint pair (QP,QΔ) — words of degree at most 2 in QP and QΔ — produces all five QT eigenspaces once their two-dimensional common kernel, on which every polynomial in the pair is scalar, is split by the top Hessian projector of the banked golden form η.", "scope": { "carrier": "Loaded-plane projector PB and the tangent-sector selector eigenspaces", "domain": "Eigenspaces as subspaces; weights and nonlinear shape are separate.", "group": null, "hypotheses": [ "PB is the registered loaded plane.", "The transport defect is ∆T = [Tϕ,PB] = [J0,PB].", "The registered joint pair is (QP,Q∆)." ], "physical_target": null, "quantifier": "The declared class only.", "real_form": "Split-real 56-frame" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 170 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix E", "section": "§7, Forced interior split", "pdf_page": 176, "quote": "PB forces the exact 26 ⊕ 10 eigenspace split" }, "caution": "This subspace construction does not select the loaded plane, the eigenvalue weights or a unique nonlinear action.", "candidate_ids": [ "C2-106" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "cited_by_section", "target": "E-C04.2.claims-used" }, { "type": "cited_by_section", "target": "E-C04.2.derivation" }, { "type": "cited_by_section", "target": "E-C04.2.prior-art" }, { "type": "cited_by_section", "target": "E-C04.2.sources-receipt" } ], "url": "/library-v2/LIB2-025/", "content_sha256": "6e402c44423cef27ba73ddccb1de78be49499cb2c80f8b086a894605311e7471", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-026", "entry_version": 11, "class": "CLAIM", "title": "A rank-character action represents the selector Hessian", "statement": "The registered rank-normalized carrier-character action Fchar has a critical point at the base with ∇²Fchar(I) = QT, and its displayed coefficients are traced to carrier ranks.", "scope": { "carrier": "Loaded plane PB, Frobenius-orthonormal p-basis and joint-defect projectors", "domain": "The displayed action and its second variation, not a uniqueness theorem for actions.", "group": null, "hypotheses": [ "PB = iB iBᵀ is the loaded plane.", "The projectors Π1,Π32,Π36 and Ξ = Π10 − Π26 are the registered joint-defect projectors.", "Fchar is the particular nonlinear functional printed in Theorem 9.1." ], "physical_target": null, "quantifier": "The declared class only.", "real_form": "Frozen split-real carrier" }, "source_labels_as_printed": { "math_status": "Certified", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 296 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix S", "section": "§9.1, Theorem 9.1: critical point and Hessian", "pdf_page": 313, "quote": "has its critical point at the base with ∇2 Fchar (I) = QT exactly" }, "caution": "A variational representation of QT does not supply a microscopic principle selecting Fchar or its nonlinear shape.", "candidate_ids": [ "C2-107" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "depends_on", "target": "LIB2-025" }, { "type": "cited_by_section", "target": "E-C04.2.claims-used" }, { "type": "cited_by_section", "target": "E-C04.2.derivation" }, { "type": "cited_by_section", "target": "E-C04.2.prior-art" }, { "type": "cited_by_section", "target": "E-C04.2.sources-receipt" } ], "url": "/library-v2/LIB2-026/", "content_sha256": "d4dd4615a4746e327c4f299e50cebf956c386c6804e44bd3d92a636fa5579360", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-027", "entry_version": 7, "class": "CLAIM", "title": "The declared action-completion class retains nonlinear-shape freedom", "statement": "In the declared rank-normalized character-completion class, actions with a critical point at the base and positive-semidefinite Hessian form, modulo equivalence, a four-dimensional moduli space: three Hessian-weight ratios and one nonlinear modulus invisible to the complete two-jet.", "scope": { "carrier": "Nonlinear actions in the declared rank-normalized character-completion class", "domain": "The declared completion class before adopting Φdiag; not every possible action class.", "group": null, "hypotheses": [ "Use the class and equivalence relation declared before the source analysis.", "Require a critical point at the base and positive-semidefinite Hessian." ], "physical_target": null, "quantifier": "The declared class only.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 297 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix S", "section": "§9.4, Theorem 9.4: moduli space", "pdf_page": 314, "quote": "the solution set of “critical point at the base + positive-semidefinite Hessian” modulo equivalence is a four-dimensional moduli space," }, "caution": "This obstruction is class-relative; enlarging the class changes its moduli count, and matching a Hessian alone does not select an action.", "candidate_ids": [ "C2-108" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-026" }, { "type": "cited_by_section", "target": "E-C04.2.claims-used" }, { "type": "cited_by_section", "target": "E-C04.2.derivation" }, { "type": "cited_by_section", "target": "E-C04.2.prior-art" }, { "type": "cited_by_section", "target": "E-C04.2.sources-receipt" } ], "url": "/library-v2/LIB2-027/", "content_sha256": "5ba75a403cc9ab5f826fd19ca3c8bee4731163dc8bc8756398cc983b5a1c8fa5", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-028", "entry_version": 8, "class": "CLAIM", "title": "The action-shape principle is adopted rather than intrinsically selected", "statement": "Within the minimal-word class, the adopted relations Φdiag = {v = 0,w = 0,u = t,27z = t} isolate the Fchar orbit, but their selection is non-intrinsic and changes under independent generator rescaling.", "scope": { "carrier": "Coefficient relations on inequivalent primitive generator lines", "domain": "The adopted action-shape section in the named class, not a consequence of ordinary equivariance.", "group": null, "hypotheses": [ "Restrict to the minimal-word class.", "Adopt v = 0, w = 0, u = t and 27z = t as the declared structural principle." ], "physical_target": null, "quantifier": "The declared class only.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 297 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" }, { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix S", "section": "§9.4, Priced axiom 9.5: adopted relations", "pdf_page": 314, "quote": "The clause Φdiag : {v = 0, w = 0, u = t, 27z = t} — four coefficient relations — isolates exactly the Fchar orbit and is minimal in codimension (dropping any one relation restores a projective one-parameter family)." }, "caution": "Adopting these relations does not derive nature's nonlinear action or remove the separate loaded boundary datum.", "candidate_ids": [ "C2-108" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-027" }, { "type": "related_to", "target": "LIB2-026" }, { "type": "cited_by_section", "target": "E-C04.2.claims-used" }, { "type": "cited_by_section", "target": "E-C04.2.derivation" }, { "type": "cited_by_section", "target": "E-C04.2.prior-art" }, { "type": "cited_by_section", "target": "E-C04.2.sources-receipt" } ], "url": "/library-v2/LIB2-028/", "content_sha256": "0f06a45b79b7018824b0ad98958891d78284585115b4c7bee38eac7a32795ad0", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-029", "entry_version": 8, "class": "CLAIM", "title": "The conditional selector for occupied golden mass-ladder rungs", "statement": "The three-layer occupation selector has support O = {0,3,11,17} and period-two continuation {31,39}, conditional on the vacuum-to-projector bridge and the banked central sign T² = −I.", "scope": { "carrier": "Golden mass-ladder rung support and its continuation", "domain": "Appendix M §7's selector; not atomic orbital filling or occupation of states by particles.", "group": null, "hypotheses": [ "The vacuum-to-projector bridge Jvac → v0 → p0 is a naturalness premise, not proved canonical.", "The central sign T² = −I is banked input.", "The selector uses the registered parity, torsion and Fano/Artin adjacency layers." ], "physical_target": null, "quantifier": "The support and continuation of the registered conditional selector.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": "Derived-conditional", "pdf_page": 6 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Paper 0", "section": "Executive State Map: occupation-selector row", "pdf_page": 6, "quote": "Occupation selector → Derived-Conditional: three-layer derivation (mod-2/5/7), Appendix M." }, "caution": "This conditional support result does not derive its vacuum-to-projector premise, a physical mass operator or atomic-state occupation.", "candidate_ids": [ "C2-068" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "cited_by_section", "target": "E-C04.2.claims-used" }, { "type": "cited_by_section", "target": "E-C04.2.derivation" }, { "type": "cited_by_section", "target": "E-C04.2.prior-art" }, { "type": "cited_by_section", "target": "E-C04.2.sources-receipt" } ], "url": "/library-v2/LIB2-029/", "content_sha256": "6135160202a5ec7f768c6c892f7ad47974df2dd3b37e7cb7123cd8e87885e600", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-030", "entry_version": 7, "class": "CLAIM", "title": "Target-triviality is forced in the minimal H2 class", "statement": "In the predeclared minimal H2 class, target-triviality of the action clause is forced rather than assumed.", "scope": { "carrier": null, "domain": "Target action only; not the coefficient map or its rank.", "group": null, "hypotheses": [ "The minimal H2 class is the one declared in Appendix E §8." ], "physical_target": null, "quantifier": "The declared class only.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 170 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix E", "section": "§8, S284 rulings: target-triviality", "pdf_page": 177, "quote": "target-triviality of the action clause is forced, not assumed, by the D1214 forced-triviality theorem (house-verified to the digit, A1527)." }, "caution": "Forced target-triviality does not select the rank or the values of the coefficient map.", "candidate_ids": [ "C2-116" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "cited_by_section", "target": "E-C04.2.claims-used" }, { "type": "cited_by_section", "target": "E-C04.2.derivation" }, { "type": "cited_by_section", "target": "E-C04.2.sources-receipt" } ], "url": "/library-v2/LIB2-030/", "content_sha256": "a69f98d6e4c422461178d2d63389612981d37f8822b3656d888c7984dba8268c", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-031", "entry_version": 8, "class": "CLAIM", "title": "The minimal H2 rank and coefficient price are predeclared", "statement": "The minimal H2 class is predeclared at rank 2, with six continuous C0 coefficients plus one-map-for-all-η naturality retained as its standing price.", "scope": { "carrier": "The minimal H2 coefficient class", "domain": "The H2 leg of the finite selector construction.", "group": null, "hypotheses": [ "The rank is predeclared, not selected by this statement." ], "physical_target": null, "quantifier": "The declared class only.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 170 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix E", "section": "§8, S284 rulings: H2 rank and price", "pdf_page": 177, "quote": "The H2 minimal-class rank is predeclared: rank 2. The H2 leg’s standing price is stated exactly: six continuous C0 coefficients plus one-map-for-all-η naturality" }, "caution": "The predeclared rank and standing price do not determine numerical coefficient values.", "candidate_ids": [ "C2-117" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-030" }, { "type": "cited_by_section", "target": "E-C04.2.claims-used" }, { "type": "cited_by_section", "target": "E-C04.2.derivation" }, { "type": "cited_by_section", "target": "E-C04.2.sources-receipt" } ], "url": "/library-v2/LIB2-031/", "content_sha256": "6741c52a6b7f161271c766847c8ba1824672b7abb15fd8a5fa840422f635995f", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-032", "entry_version": 8, "class": "CLAIM", "title": "The frozen H2 conditions do not select the coefficient map", "statement": "At the frozen H2 tier, two disjoint symbolic candidates of rank 2 pass the same 13 gates and 30 controls, and no banked selection polynomial separates them.", "scope": { "carrier": "The two symbolic rank-two coefficient-map candidates", "domain": "The scoped coefficient-independence result, not every possible higher-tier source law.", "group": null, "hypotheses": [ "The H2 tier, gates, controls and banked selection-polynomial inventory are frozen." ], "physical_target": null, "quantifier": "The declared class only.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 171 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix E", "section": "§8, C0 independence theorem", "pdf_page": 177, "quote": "At the frozen H2 tier the six-coefficient freedom is countermodel-grade: two disjoint symbolic rank-2 candidates pass all 13 gates and 30 controls identically, and no banked selection polynomial separates them" }, "caution": "A higher-tier Sjoint, if supplied, may still derive the coefficients; the present countermodels do not exclude it.", "candidate_ids": [ "C2-118" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-031" }, { "type": "cited_by_section", "target": "E-C04.2.claims-used" }, { "type": "cited_by_section", "target": "E-C04.2.derivation" }, { "type": "cited_by_section", "target": "E-C04.2.prior-art" }, { "type": "cited_by_section", "target": "E-C04.2.sources-receipt" } ], "url": "/library-v2/LIB2-032/", "content_sha256": "1059963442cf9df8b765b6459a8245428ce33e2d7986d305e8e1ef0700ba47d7", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-033", "entry_version": 7, "class": "CLAIM", "title": "The banked refined-condition inventory does not select Φdiag", "statement": "No refined condition family in the current banked class and condition inventory selects Φdiag non-circularly.", "scope": { "carrier": "The action-shape condition inventory", "domain": "The banked F-SEL(c) search, not all future invariant or condition families.", "group": null, "hypotheses": [ "Use the filed condition inventory described in Appendix E §8.", "Word minimality is already an adopted class restriction." ], "physical_target": null, "quantifier": "The declared class only.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 172 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix E", "section": "§8, F-SEL(c): scoped closure", "pdf_page": 178, "quote": "no banked refined condition family selects Φdiag non-circularly. F-SEL(c) closes negative at the current banked class and condition inventory." }, "caution": "This is not a universal impossibility theorem; a genuinely new, independently derived invariant or condition family can reopen it.", "candidate_ids": [ "C2-121" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-028" }, { "type": "cited_by_section", "target": "E-C04.2.claims-used" }, { "type": "cited_by_section", "target": "E-C04.2.derivation" }, { "type": "cited_by_section", "target": "E-C04.2.prior-art" }, { "type": "cited_by_section", "target": "E-C04.2.sources-receipt" } ], "url": "/library-v2/LIB2-033/", "content_sha256": "c894a32550aac8ae7f54016a6a88e1845e1819a657ac1e1a5b1113a18ebecf40", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-034", "entry_version": 7, "class": "CLAIM", "title": "Casimir-naturality excludes the adopted action-shape target", "statement": "In the declared coefficient class, imposing A = f(CKdyn) excludes the nonzero Φdiag target rather than selecting it.", "scope": { "carrier": "The coefficient carrier p70 and its Kdyn Casimir", "domain": "Both source-stated readings exclude the nonzero target.", "group": "Kdyn", "hypotheses": [ "A is constrained to be a function of the Kdyn Casimir.", "The nonzero target obeys 27z = t.", "The support-69 reading is an additional priced premise, not the literal full-carrier class." ], "physical_target": null, "quantifier": "The declared class only.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 172 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix E", "section": "§8, Casimir-naturality: conclusion", "pdf_page": 178, "quote": "Casimir-naturality excludes Φdiag ; it is a refuter, not a selector" }, "caution": "Casimir-naturality is an additional multiplicity-blind principle, not a consequence of ordinary equivariance.", "candidate_ids": [ "C2-121" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-028" }, { "type": "related_to", "target": "LIB2-033" }, { "type": "cited_by_section", "target": "E-C04.2.claims-used" }, { "type": "cited_by_section", "target": "E-C04.2.derivation" }, { "type": "cited_by_section", "target": "E-C04.2.sources-receipt" } ], "url": "/library-v2/LIB2-034/", "content_sha256": "bf3576d9d525856baad5c51d1a6e6efb1b57ff9109109ed7df59256757cc3d48", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-035", "entry_version": 8, "class": "CLAIM", "title": "The banked non-degenerate stability conditions leave an interior", "statement": "The banked non-degenerate PSD/stability inequalities have non-empty interior, leaving a 6-dimensional feasible set before the scale quotient and a 5-dimensional set after it; they do not select a ray.", "scope": { "carrier": "The coefficient tuple (t,t2,u,v,w,z)", "domain": "The particular non-degenerate inequality system, not inequalities in general.", "group": null, "hypotheses": [ "Use the five inequalities printed in Appendix E §8.", "The displayed strict-interior witness is (1,1,1,1,1,0)." ], "physical_target": null, "quantifier": "The declared class only.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 171 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix E", "section": "§8, Corrected non-degenerate positivity argument", "pdf_page": 178, "quote": "the feasible set is 6-dimensional before the scale quotient and 5- dimensional after it, and cannot select a ray." }, "caution": "Degenerate inequalities can encode equalities, so this result is not a universal ban on dimension-reducing inequality constraints.", "candidate_ids": [ "C2-121" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-033" }, { "type": "cited_by_section", "target": "E-C04.2.claims-used" }, { "type": "cited_by_section", "target": "E-C04.2.derivation" }, { "type": "cited_by_section", "target": "E-C04.2.prior-art" }, { "type": "cited_by_section", "target": "E-C04.2.sources-receipt" } ], "url": "/library-v2/LIB2-035/", "content_sha256": "4f2f1cde39cc082f4dbfcad0d84d333188aca6950370608df622b2e824b48a7a", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-036", "entry_version": 7, "class": "CLAIM", "title": "An action depending only on the registered Gram map cannot select a coset point", "statement": "No action factoring only through the registered Gram map GB can uniquely select a coset point, because its two-dimensional dark fibre is invisible to that map.", "scope": { "carrier": "GB(M) = iBᵀ M iB on the registered scalar coset", "domain": "The GB-factoring subclass at every order; wider parent actions and boundary laws are excluded from this claim.", "group": null, "hypotheses": [ "The action factors only through GB.", "The registered map has the dark fibre reported in Appendix E §6(i)." ], "physical_target": null, "quantifier": "The declared class only.", "real_form": "E7(7)/SU(8)" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 166 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix E", "section": "§6(i), Gram-only selector obstruction", "pdf_page": 172, "quote": "Consequently no action factoring only through GB can uniquely select a coset point — not obstructed at some order, but dead at every order." }, "caution": "This exclusion does not apply to parent actions that use additional full-carrier or boundary information.", "candidate_ids": [ "C2-105" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-021" }, { "type": "cited_by_section", "target": "E-C04.2.claims-used" }, { "type": "cited_by_section", "target": "E-C04.2.derivation" }, { "type": "cited_by_section", "target": "E-C04.2.prior-art" }, { "type": "cited_by_section", "target": "E-C04.2.sources-receipt" } ], "url": "/library-v2/LIB2-036/", "content_sha256": "909ab69958186f61db3b17438e4dbcd60c00a280fe99a1f2eba0d798bc24fc23", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-037", "entry_version": 7, "class": "CLAIM", "title": "The declared frame-free invariant class has no nonzero dark response", "statement": "The declared class Cff of twice-differentiable scalars invariant under the diagonal E7(7) action, with no spurion and a point source space, has no law with a nonzero dark response.", "scope": { "carrier": "(E7(7)/SU(8)) × OB", "domain": "The predeclared Cff class, not a basepointed full-carrier law.", "group": "Diagonal E7(7)", "hypotheses": [ "The scalar is twice differentiable and invariant under the diagonal E7(7) action.", "There is no spurion, and the source space is a point." ], "physical_target": null, "quantifier": "The declared class only.", "real_form": "E7(7)/SU(8)" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 166 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix E", "section": "§6(ii), Frame-free diagonal-invariant scalar class", "pdf_page": 173, "quote": "For the class Cff of C 2 scalars on (E7(7) /SU (8)) × OB that are invariant under the diagonal E7(7) action, with no spurion and a point source space — declared before testing — there is no law with a nonzero dark response:" }, "caution": "A basepointed full-carrier response exists outside this frame-free reading; its basepoint is convention-loaded.", "candidate_ids": [ "C2-105" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-036" }, { "type": "cited_by_section", "target": "E-C04.2.claims-used" }, { "type": "cited_by_section", "target": "E-C04.2.derivation" }, { "type": "cited_by_section", "target": "E-C04.2.sources-receipt" } ], "url": "/library-v2/LIB2-037/", "content_sha256": "0248dcee47a0bf641325f2de9de0f5718a9e3511a14cb06c03985e8019ef353c", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-038", "entry_version": 8, "class": "CLAIM", "title": "The transported selector consumes a source without selecting its ray", "statement": "In the declared transported quadratic/current class, equal-norm sources share the minimum value, transport price and local spectrum, so the functional consumes j but cannot select its source ray.", "scope": { "carrier": "The transported loaded plane and its source j", "domain": "The transported selector functional, not the later extended conditional parent action.", "group": null, "hypotheses": [ "The transported quadratic/current class is fixed.", "Its constants use the declared conditioning–minimax principle." ], "physical_target": null, "quantifier": "The declared class only.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 166 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix E", "section": "§6(iii), Transported-selector source isotropy", "pdf_page": 173, "quote": "equal-norm sources share the minimum value, the transport price and the local spectrum. The transported quadratic/current class consumes j and cannot select its ray." }, "caution": "This source-isotropy result does not negate the later finite conditional parent-action extension or supply an intrinsic boundary datum.", "candidate_ids": [ "C2-105" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-021" }, { "type": "related_to", "target": "LIB2-022" }, { "type": "cited_by_section", "target": "E-C04.2.claims-used" }, { "type": "cited_by_section", "target": "E-C04.2.derivation" }, { "type": "cited_by_section", "target": "E-C04.2.sources-receipt" } ], "url": "/library-v2/LIB2-038/", "content_sha256": "95ef268eb780db8c4a2a125da2025904a89847db0ee5b7e085a14db3f362e599", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-039", "entry_version": 7, "class": "CLAIM", "title": "A fixed-grade cubic/current law cannot detect both dark directions", "statement": "In the declared fixed-grade cubic/current class, restriction to grade +2 gives rank 1 for Z ↦ P27 Z P27, so it cannot provide rank-two detection of the registered dark fibre.", "scope": { "carrier": "The dark fibre restricted to the fixed +2 grade", "domain": "Rank-two detection inside a fixed grade; the embedding-tensor class was not decided.", "group": null, "hypotheses": [ "The detector stays inside the fixed grade and uses the declared cubic/current class.", "Both registered dark directions are required for rank-two detection." ], "physical_target": null, "quantifier": "The declared class only.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 167 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix E", "section": "§6(iv), Fixed-grade detection obstruction", "pdf_page": 173, "quote": "The fixed-grade cubic/current class is closed negative for rank-two detection (s1005–s1006)." }, "caution": "This fixed-grade exclusion is not an embedding-tensor no-go; that separate class was scoped out for lack of a convention-certified branching artifact.", "candidate_ids": [ "C2-105" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-036" }, { "type": "cited_by_section", "target": "E-C04.2.claims-used" }, { "type": "cited_by_section", "target": "E-C04.2.derivation" }, { "type": "cited_by_section", "target": "E-C04.2.sources-receipt" } ], "url": "/library-v2/LIB2-039/", "content_sha256": "2a70a1aa8b3bc411025169b35c38b30059e7baaacd0d85ab6a12e8b845fba4fa", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-040", "entry_version": 8, "class": "CLAIM", "title": "An RB-even action cannot select the horizontal-orbit sign", "statement": "For X in the registered horizontal 16-dimensional sector, every RB-conjugation-invariant scalar obeys S(exp(2tX)) = S(exp(−2tX)), so an RB-even action cannot resolve that sign.", "scope": { "carrier": "The horizontal 16-dimensional sector and its exponential orbit", "domain": "The horizontal sign pair in the declared even-action class.", "group": null, "hypotheses": [ "RB e^(2tX) RB = e^(-2tX) in the registered carrier.", "S is invariant under RB conjugation." ], "physical_target": null, "quantifier": "The declared class only.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 167 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix E", "section": "§6(v), Even-action sign obstruction", "pdf_page": 173, "quote": "An RB -even action cannot resolve the sign — the parity of the law, not its strength, is what fails." }, "caution": "This symmetry obstruction requires an RB-odd ingredient somewhere; it does not itself construct or select that ingredient.", "candidate_ids": [ "C2-105" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "cited_by_section", "target": "E-C04.2.claims-used" }, { "type": "cited_by_section", "target": "E-C04.2.derivation" }, { "type": "cited_by_section", "target": "E-C04.2.prior-art" }, { "type": "cited_by_section", "target": "E-C04.2.sources-receipt" } ], "url": "/library-v2/LIB2-040/", "content_sha256": "f1b7528434a495572f8ab5326545f4ebecf65eb5891c196bb308676232cbe6c6", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-041", "entry_version": 12, "class": "CLAIM", "title": "A frame-free invariant does not select the ordered Peirce frame", "statement": "A frame-free F4-invariant can at best select the spectral orbit of Jvac, not its ordered frame; at a stationary point on the registered orbit it has at least 24 Hessian zero modes.", "scope": { "carrier": "The ordered triple and its automorphism orbit", "domain": "Ordered-frame selection in the declared invariant class.", "group": "F4 automorphism action as printed", "hypotheses": [ "The scalar is invariant under the frame-free F4 automorphism action as printed.", "The source identifies a 24-dimensional orbit of the ordered triple." ], "physical_target": null, "quantifier": "The declared class only.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 167 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" }, { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix E", "section": "§6(vi), Frame-free orbit obstruction", "pdf_page": 174, "quote": "a frame-free F4 -invariant can at best select the spectral orbit [Jvac ]F4 ; it can never isolate the ordered frame diag(φ, 1, φ−1 )." }, "caution": "Selecting an ordered frame requires a loading or symmetry-breaking tensor; this result does not exclude selection with that additional datum.", "candidate_ids": [ "C2-102" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-019" }, { "type": "related_to", "target": "LIB2-020" }, { "type": "cited_by_section", "target": "E-C04.1.claims-used" }, { "type": "cited_by_section", "target": "E-C04.1.derivation" }, { "type": "cited_by_section", "target": "E-C04.1.prior-art" }, { "type": "cited_by_section", "target": "E-C04.1.sources-receipt" } ], "url": "/library-v2/LIB2-041/", "content_sha256": "5fc660466ebc218e3384ff92c10c25f4567bc762fc17006b022a47a13e7243ad", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-042", "entry_version": 9, "class": "CLAIM", "title": "A norm-only action leaves the regular norm-level directions flat", "statement": "For a twice-differentiable norm-only action S = F(α,N(X)), ambient stationarity in X at a regular norm-one point forces Hess S to vanish on ker dN, leaving at least 26 flats.", "scope": { "carrier": "Regular norm-level tangent directions in the stated cubic carrier", "domain": "The norm-only action subclass, not general invariant or source-dependent actions.", "group": null, "hypotheses": [ "S depends on X only through N(X), with the other argument α fixed.", "The point is stationary, regular and norm-one." ], "physical_target": null, "quantifier": "The declared class only.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 167 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix E", "section": "§6(vi), Norm-only Hessian obstruction", "pdf_page": 174, "quote": "for any C 2 action S = F (α, N (X)), ambient stationarity in X at a regular norm-one point forces FN = 0 and hence Hess S ≡ 0 on ker dN , giving at least 26 flats structurally." }, "caution": "The source check is on a generic symmetric cubic, not a dedicated full-Jordan computation, and the conclusion is limited to norm-only actions.", "candidate_ids": [ "C2-102" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-041" }, { "type": "cited_by_section", "target": "E-C04.1.claims-used" }, { "type": "cited_by_section", "target": "E-C04.1.prior-art" }, { "type": "cited_by_section", "target": "E-C04.1.sources-receipt" } ], "url": "/library-v2/LIB2-042/", "content_sha256": "0d50f5d03f3ab8dd4ec4e8ce1a2c210b81cf23aff57ce42a38b9a93816e4408a", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-043", "entry_version": 7, "class": "CLAIM", "title": "Unshifted quadratic Kempf–Ness potentials fail the selector-rank test", "statement": "In the declared unshifted zero-level quadratic-carrier Kempf–Ness class, rank Hess0∥µK∥² ≤ dim K ≤ 63 < 69 = rank QT, so this class cannot reproduce the selector Hessian.", "scope": { "carrier": "The unshifted zero-level quadratic carrier and its moment-map-square potential", "domain": "The unshifted zero-level quadratic-carrier class only.", "group": "K in the declared class", "hypotheses": [ "Use the predeclared Kempf–Ness class cited in Appendix E §6(vii).", "The target is the registered selector Hessian QT." ], "physical_target": null, "quantifier": "The declared class only.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 167 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix E", "section": "§6(vii), Unshifted Kempf–Ness rank bound", "pdf_page": 174, "quote": "rank Hess0 ∥µK ∥2 ≤ dim K ≤ 63 < 69 = rank QT (the rank no-go)" }, "caution": "Central shifts on proper subgroups or departure from the declared carrier/potential class are not excluded by this bound.", "candidate_ids": [ "C2-108" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-027" }, { "type": "cited_by_section", "target": "E-C04.2.claims-used" }, { "type": "cited_by_section", "target": "E-C04.2.derivation" }, { "type": "cited_by_section", "target": "E-C04.2.prior-art" }, { "type": "cited_by_section", "target": "E-C04.2.sources-receipt" } ], "url": "/library-v2/LIB2-043/", "content_sha256": "aaf434e33d4198b90c2d62901d11f78c9252c172d75b205a614feee63ab8cd3a", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-044", "entry_version": 7, "class": "CLAIM", "title": "A beat-invariant potential in the declared KN class cannot isolate the dark ray", "statement": "In the declared unshifted zero-level quadratic-carrier Kempf–Ness class, no beat-invariant potential isolates the selector ray [W0].", "scope": { "carrier": "The beat orbit and selector ray [W0]", "domain": "The source-stated beat-transitivity obstruction; separate from the Hessian-rank bound.", "group": null, "hypotheses": [ "Use the declared unshifted zero-level quadratic-carrier Kempf–Ness class.", "The potential is beat-invariant." ], "physical_target": null, "quantifier": "The declared class only.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 167 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix E", "section": "§6(vii), Beat-transitivity obstruction", "pdf_page": 174, "quote": "no beat-invariant KN potential isolates [W0 ] (the beat-transitivity no-go)." }, "caution": "A beat-breaking spurion, dropping the clock circle or leaving the KN family exits this declared class; none is ruled out universally.", "candidate_ids": [ "C2-108" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-043" }, { "type": "related_to", "target": "LIB2-023" }, { "type": "cited_by_section", "target": "E-C04.2.claims-used" }, { "type": "cited_by_section", "target": "E-C04.2.derivation" }, { "type": "cited_by_section", "target": "E-C04.2.sources-receipt" } ], "url": "/library-v2/LIB2-044/", "content_sha256": "d4e98a452d2f50b944fa8f88e65e1b73115b22acf971b839d2239607beda1d5c", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-045", "entry_version": 8, "class": "CLAIM", "title": "The braid/trace grammar cannot select the boundary source datum", "statement": "No construction internal to the registered braid/trace grammar selects the boundary source ray [j] or its equivalent descriptions L∂ and E*, because the source-ray symmetry remains transitive.", "scope": { "carrier": "The boundary source datum [j] ⇔ L∂ ⇔ E* and its braid-fixed carrier", "domain": "Intrinsic boundary-source selection within the grammar, not genuinely external categories.", "group": null, "hypotheses": [ "Only constructions internal to the registered braid/trace grammar are admitted.", "The source reports O(16) transitivity on source rays and SO(16) transitivity already on the source sphere." ], "physical_target": null, "quantifier": "The declared class only.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 169 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix E", "section": "§7, Boundary-source obstruction", "pdf_page": 175, "quote": "no construction internal to the braid/trace grammar can select [j], L∂ , or E ∗ . The boundary price is irreducible within the grammar. Scope: genuinely external categories are not excluded." }, "caution": "The grammar can select the separate dark ray; this obstruction concerns the loaded boundary datum and does not exclude external selection laws.", "candidate_ids": [ "C2-105" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-022" }, { "type": "related_to", "target": "LIB2-023" }, { "type": "cited_by_section", "target": "E-C04.2.claims-used" }, { "type": "cited_by_section", "target": "E-C04.2.derivation" }, { "type": "cited_by_section", "target": "E-C04.2.prior-art" }, { "type": "cited_by_section", "target": "E-C04.2.sources-receipt" } ], "url": "/library-v2/LIB2-045/", "content_sha256": "90ee0598f5fe570a5967e2bd28658a75f97fc87f6d956f589e2b540fecfbd560", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-046", "entry_version": 7, "class": "CLAIM", "title": "The golden spectrum obeys the reciprocal-square identity", "statement": "The selected golden spectrum satisfies the exact internal identity ϕ² + ϕ⁻² = 3.", "scope": { "carrier": "The positive golden vacuum spectrum", "domain": "The exact spectral identity, distinct from its solar-angle application.", "group": null, "hypotheses": [ "The vacuum has the selected spectrum {ϕ,1,ϕ⁻¹}." ], "physical_target": null, "quantifier": "The registered construction only.", "real_form": "J3(Os)" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 165 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "analytic", "availability": "shipped" } ], "primary_source": { "component": "Appendix E", "section": "§5, Corollary 1: spectral identity", "pdf_page": 172, "quote": "ϕ2 + ϕ−2 = 3," }, "caution": "This internal identity does not by itself select the physical readout or remove the hypotheses of the vacuum-selector theorem.", "candidate_ids": [ "C2-001" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-019" }, { "type": "related_to", "target": "LIB2-020" }, { "type": "cited_by_section", "target": "E-C05.1.claims-used" }, { "type": "cited_by_section", "target": "E-C05.1.prior-art" } ], "url": "/library-v2/LIB2-046/", "content_sha256": "94f73d745a891bd21314af18246963779b6c82173b8bed947fdb0d303b08e814", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-047", "entry_version": 7, "class": "CLAIM", "title": "The working golden vacuum has unit Jordan determinant", "statement": "At the working vacuum Jvac = diag(ϕ,1,ϕ⁻¹), the Jordan determinant is det Jvac = 1.", "scope": { "carrier": "The diagonal golden Jordan vacuum", "domain": "The determinant identity, not a new vacuum-selection law.", "group": null, "hypotheses": [ "Use the working vacuum diag(ϕ,1,ϕ⁻¹) and the Jordan determinant." ], "physical_target": null, "quantifier": "The registered construction only.", "real_form": "J3(Os)" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 25 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "analytic", "availability": "shipped" } ], "primary_source": { "component": "Paper 1", "section": "§3, Roman-surface paragraph: vacuum adjoint", "pdf_page": 26, "quote": "The vacuum Jvac = diag(ϕ, 1, ϕ−1 ) satisfies Jvac # = diag(ϕ−1 , 1, ϕ) = J −1 (Jordan inverse), consistent vac with det Jvac = 1." }, "caution": "Unit determinant alone does not select the golden spectrum; Appendix E uses it as a normalization hypothesis.", "candidate_ids": [ "C2-002" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "cited_by_section", "target": "E-C02.2.claims-used" }, { "type": "cited_by_section", "target": "E-C02.2.derivation" }, { "type": "cited_by_section", "target": "E-C02.2.prior-art" }, { "type": "cited_by_section", "target": "E-C05.1.prior-art" } ], "url": "/library-v2/LIB2-047/", "content_sha256": "f1f16ca6fbecd42f4d9829f442101dc75965ec9e03ece4928375d4f7d42af1aa", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-048", "entry_version": 7, "class": "CLAIM", "title": "The selected Jordan vacuum pair has Gram determinant seven", "statement": "For the selected Jordan pair (Jvac,Jvac#), the trace-form Gram determinant is 7.", "scope": { "carrier": "The Jordan vacuum and adjoint pair", "domain": "Internal Gram evaluation.", "group": null, "hypotheses": [ "Use the selected golden vacuum, its Jordan adjoint and the registered trace form." ], "physical_target": null, "quantifier": "The registered construction only.", "real_form": "J3(Os)" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 153 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "analytic", "availability": "shipped" } ], "primary_source": { "component": "Appendix B", "section": "§B.5, Structural support (a): DET-7", "pdf_page": 159, "quote": "The Jordan pair (Jvac , Jvac # ) has Gram determinant 7, fixing the mismatch geometry and the normalization of the (1, 3) sector." }, "caution": "The Gram value does not derive the physical atmospheric registration and is distinct from imposing DET-7 as a selector premise.", "candidate_ids": [ "C2-003" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-046" }, { "type": "related_to", "target": "LIB2-047" }, { "type": "related_to", "target": "LIB2-018" }, { "type": "cited_by_section", "target": "E-C05.1.claims-used" }, { "type": "cited_by_section", "target": "E-C05.1.prior-art" } ], "url": "/library-v2/LIB2-048/", "content_sha256": "fb2ce4548e60b84b6e8f0e72dd196c0347d2eb1b7e862d08650dab5aefdd8dd5", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-049", "entry_version": 7, "class": "CLAIM", "title": "The octonion-dimension to Jordan-rank ratio is an internal identity", "statement": "The ratio dim(Os)/rank(J3) equals 8/3 as an exact dimension ratio.", "scope": { "carrier": "Split octonion dimension and Jordan rank", "domain": "Dimension ratio only.", "group": null, "hypotheses": [ "Use the dimensions and rank in the printed Jordan-algebra normalization." ], "physical_target": null, "quantifier": "The registered construction only.", "real_form": "Os and J3(Os)" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 148 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix A", "section": "§A.9, Exact dimension ratio", "pdf_page": 154, "quote": "where p = 8/3 = dim(Os )/rank(J3 ) is an exact dimension ratio [A616]" }, "caution": "An exact dimension ratio is not by itself a physical mass exponent.", "candidate_ids": [ "C2-056" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "cited_by_section", "target": "E-C05.1.claims-used" }, { "type": "cited_by_section", "target": "E-C05.1.prior-art" } ], "url": "/library-v2/LIB2-049/", "content_sha256": "ff9d2a92e3df0e76daaff0e75038732fb9ee041c170fca2c643d1899ed02e485", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-050", "entry_version": 7, "class": "CLAIM", "title": "The Peirce first-row weight factors into trace and generation normalizations", "statement": "The registered Peirce first-row weight is the exact product 1/√6 = (1/√2)(1/√3), combining the trace-form block and three-generation normalization.", "scope": { "carrier": "Registered Peirce first-row trace-form block and generation normalization", "domain": "The first-row weight, not the full CKM correspondence.", "group": null, "hypotheses": [ "Use the registered first-row Peirce block and three-generation normalization." ], "physical_target": null, "quantifier": "The registered construction only.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 46 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Paper 3", "section": "Abstract, Rev29 update: Route-B weight", "pdf_page": 48, "quote": "1/ 6 factorises as 1/ 2 · 1/ 3 = 1/ 3! (s499): the 1/ 2 trace-form block times the 1/ 3 three- generation normalisation — a derived product, independent of any kaon fit." }, "caution": "The exact weight does not select the first-row route or establish a universal block-weight functor.", "candidate_ids": [ "C2-062" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "cited_by_section", "target": "E-C05.1.claims-used" }, { "type": "cited_by_section", "target": "E-C05.1.derivation" }, { "type": "cited_by_section", "target": "E-C05.1.prior-art" } ], "url": "/library-v2/LIB2-050/", "content_sha256": "f8dda60daa36f01ed5576fca67c5bce0428906a2e8832b5478550473ec9f0b39", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-051", "entry_version": 9, "class": "CLAIM", "title": "The registered half-weight generator has fixed octonionic coefficient", "statement": "In the registered generator Thalf = Tscalar + c Toct, the C1 weight is exactly c = 1/2.", "scope": { "carrier": "The registered scalar and octonionic parts of Thalf", "domain": "The internal C1 coefficient, not its physical phase readout.", "group": null, "hypotheses": [ "Use the registered generator normalization, DET-7 ratio, Frobenius norm and Peirce orthogonality." ], "physical_target": null, "quantifier": "The registered construction only.", "real_form": "f4(4)" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 153 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix B", "section": "§B.5, Structural support (b): C1 weight", "pdf_page": 159, "quote": "The weight c = 12 in Thalf = Tscalar + 12 Toct is exact, so the generator is fixed with no free coefficient." }, "caution": "Fixing this internal coefficient does not derive the framing choice or its identification with a measured Dirac phase.", "candidate_ids": [ "C2-158" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "cited_by_section", "target": "E-C05.1.claims-used" }, { "type": "cited_by_section", "target": "E-C05.1.derivation" }, { "type": "cited_by_section", "target": "E-C05.1.prior-art" }, { "type": "rests_on_premise", "target": "PRM-013" } ], "url": "/library-v2/LIB2-051/", "content_sha256": "11054913301869970dd594c73fb95f8cede5791a09c1d33d60bc988e65e6f0b9", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-052", "entry_version": 8, "class": "CLAIM", "title": "The fixed Peirce sector has the registered unique invariant generator", "statement": "Within the registered (1,3) Peirce-sector construction of f4(4), Thalf is, up to scale, the unique G2(2)-invariant generator; the scale is fixed by the normalisation Thalf = Tscalar + ½Toct.", "scope": { "carrier": "The registered (1,3) Peirce-sector generator", "domain": "The internal generator construction.", "group": "G2(2)", "hypotheses": [ "The (1,3) sector and the registered Thalf normalization are fixed." ], "physical_target": null, "quantifier": "The registered construction only.", "real_form": "f4(4)" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 153 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix B", "section": "§B.5, Structural support (c): generator uniqueness", "pdf_page": 159, "quote": "Thalf is, up to scale, the unique G2(2) -invariant generator in the (1, 3) Peirce sector of f4(4) ; the scale is the normalisation Thalf = Tscalar + 12 Toct of the item above (Rev32.9)." }, "caution": "Sector-relative uniqueness does not select the sector itself or prove the physical phase attachment.", "candidate_ids": [ "C2-158" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-051" }, { "type": "cited_by_section", "target": "E-C05.1.claims-used" }, { "type": "cited_by_section", "target": "E-C05.1.derivation" }, { "type": "cited_by_section", "target": "E-C05.1.prior-art" } ], "url": "/library-v2/LIB2-052/", "content_sha256": "8b9ff2be1bb2157b24b7fa761901c94c33d2b0f1756ed498e3f99ee225d26410", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-053", "entry_version": 8, "class": "CLAIM", "title": "Frobenius compatibility fixes the finite trace ratio", "statement": "On the reflected module 1 ⊕ 3 ⊕ 3̄, the registered Frobenius identity forces the trace weights a = b, uniquely fixing the readout r = 2 + b/(3a) = 7/3.", "scope": { "carrier": "The reflected module 1 ⊕ 3 ⊕ 3̄ and its trace weights", "domain": "The nonzero normalized trace readout of Theorem 4.3.", "group": null, "hypotheses": [ "Use the reflected trace-weight class τa,b and the exact registered Zorn product.", "Impose the Frobenius compatibility identity in the source normalization." ], "physical_target": null, "quantifier": "The registered construction only.", "real_form": "Split-octonion Zorn product" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 232 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix K", "section": "§4, Theorem 4.3: reflected trace weight", "pdf_page": 244, "quote": "r = 2 + b/(3a)." }, "caution": "The unique finite trace normalization is not an LSZ residue, a low-energy mass theorem or a derived physical export.", "candidate_ids": [ "C2-044", "C2-054" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "cited_by_section", "target": "E-C05.1.claims-used" }, { "type": "cited_by_section", "target": "E-C05.1.derivation" }, { "type": "cited_by_section", "target": "E-C05.1.prior-art" }, { "type": "cited_by_section", "target": "E-C08.2.claims-used" }, { "type": "cited_by_section", "target": "E-C08.2.definitions-conventions" }, { "type": "cited_by_section", "target": "E-C08.2.prior-art" } ], "url": "/library-v2/LIB2-053/", "content_sha256": "7633c7a40ce027a15df823a8272335a2703652204d13479a18d9563e63603472", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-054", "entry_version": 8, "class": "CLAIM", "title": "The finite tick has an additive mirror-reversing grading", "statement": "The banked clock weight is an exact Z4-valued grading, additive under composition and reversed by the mirror on the full registered generator set.", "scope": { "carrier": "The banked winding-category generators", "domain": "An internal grading, not a spacetime identification.", "group": "Z4 grading", "hypotheses": [ "Use the registered composition and mirror operations on the full generator set." ], "physical_target": null, "quantifier": "The full registered generator set.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 269 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix P", "section": "§2, Theorem 2.1: tick grading", "pdf_page": 284, "quote": "The Z4 clock weight of the banked grading behaves as a momentum-like quantum number modulo 4: the grading law, additivity under composition, and reversal under the mirror are all exact on the full generator set." }, "caution": "This grading is not a physical momentum conjugate to a constructed compact coordinate.", "candidate_ids": [ "C2-029" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "cited_by_section", "target": "E-C05.2.claims-used" }, { "type": "cited_by_section", "target": "E-C05.2.prior-art" }, { "type": "cited_by_section", "target": "E-C05.2.sources-receipt" } ], "url": "/library-v2/LIB2-054/", "content_sha256": "7c086a7c8178e69bdb1ca0c8b4313ba6907e02a39282aa9235ed36c3a474367c", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-055", "entry_version": 8, "class": "CLAIM", "title": "The finite carrier fails the cylinder-condition count", "statement": "The banked carrier requires the invariant dimension signature (1,27,27,1), whose count does not close on the cylinder-invariant subspace.", "scope": { "carrier": "The banked invariant carrier decomposition", "domain": "The finite cylinder-condition test, not its interpretive Kaluza–Klein reading.", "group": null, "hypotheses": [ "Use the invariant decomposition and cylinder-invariant subspace specified in the banked model." ], "physical_target": null, "quantifier": "The registered construction only.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 269 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix P", "section": "§2, Theorem 2.2: cylinder-condition count", "pdf_page": 284, "quote": "The classical Kaluza–Klein cylinder condition (no dependence on the internal coordinate) is inconsistent with the banked content: the required invariant decomposition has dimension signature (1, 27, 27, 1), and the count does not close on the cylinder-invariant subspace." }, "caution": "The count is a statement about banked objects, not a proof that physical spacetime has an additional dimension.", "candidate_ids": [ "C2-025" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-054" }, { "type": "cited_by_section", "target": "E-C05.2.claims-used" }, { "type": "cited_by_section", "target": "E-C05.2.derivation" }, { "type": "cited_by_section", "target": "E-C05.2.prior-art" }, { "type": "cited_by_section", "target": "E-C05.2.sources-receipt" } ], "url": "/library-v2/LIB2-055/", "content_sha256": "26c9b76031b0134c76fa2b46d93fab4e61b2e736c64884fb614568fbdc04e9b2", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-056", "entry_version": 8, "class": "CLAIM", "title": "The selected winding symmetry model has one scale class", "statement": "For the banked Sym(Wind) census with ncyl = 2, the scale-class count is dim H²(Sym;R+) = 1, with the area cocycle as generator.", "scope": { "carrier": "The banked winding symmetry census and its area cocycle", "domain": "One cohomology class in the selected symmetry model, not an exhaustive physical input census.", "group": "Sym(Wind) as registered", "hypotheses": [ "Use the banked Sym(Wind) identification and its two-cylinder census." ], "physical_target": null, "quantifier": "The registered construction only.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 269 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix P", "section": "§2, Theorem 2.4: census and cocycle", "pdf_page": 285, "quote": "banked symmetry census (ncyl = 2): the generator is the area cocycle; the physical (both-flip) mirror preserves the class;" }, "caution": "The count does not establish exhaustiveness of the symmetry model or determine the numerical value of the physical scale.", "candidate_ids": [ "C2-028", "C2-069", "C2-080" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "cited_by_section", "target": "E-C05.2.claims-used" }, { "type": "cited_by_section", "target": "E-C05.2.prior-art" }, { "type": "cited_by_section", "target": "E-C05.2.sources-receipt" } ], "url": "/library-v2/LIB2-056/", "content_sha256": "a8a7aef7838955ddcb4494ec2daa7377e6fdad4fad745d98ca191ef69d98492f", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-057", "entry_version": 9, "class": "CLAIM", "title": "The retained PSL class-algebra coefficients", "statement": "For input classes (4A,7A), the PSL(2,7) class-algebra coefficient for output class 7A is 14, and the coefficient for output class 7B is 0.", "scope": { "carrier": "The PSL(2,7) class algebra", "domain": "Retained pure algebra in the historical paper, not an operative phase-selection mechanism.", "group": "PSL(2,7)", "hypotheses": [ "Use the source's conjugacy-class labels and character-table class-algebra normalization." ], "physical_target": null, "quantifier": "The two displayed coefficients.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 118 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 8", "section": "§2, PSL(2,7) class-algebra structure constants", "pdf_page": 122, "quote": "7A 7B c4A,7A = 14, c4A,7A = 0." }, "caution": "These coefficients neither derive the current leptonic phase nor establish a mechanism relating their value to G2.", "candidate_ids": [ "C2-172" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-057/", "content_sha256": "0bb1a79889219d126a9216be8a8554081c85a555b2e05308b9c08b9f0430ac02", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-058", "entry_version": 8, "class": "CLAIM", "title": "The cubic scaling model has a constant homogeneity derivative", "statement": "For the scaling action S = c N(J) on J3(Os), the substitution J → c^{1/3}J gives, formally, Z(c) = c⁻⁹ Z(1) and c d(log Z(c))/dc = −9; the identity holds only for a regulator or integration domain that respects the scaling.", "scope": { "carrier": "The cubic-norm scaling model on J3(Os)", "domain": "The bare-coupling homogeneity identity.", "group": null, "hypotheses": [ "Use the source's scaling action and its formal partition-function normalization.", "The real carrier dimension is 27 and the norm has degree 3." ], "physical_target": null, "quantifier": "The stated scaling model.", "real_form": "J3(Os)" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 208 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix I", "section": "§6, Proposition 6.1: scaling setup", "pdf_page": 218, "quote": "For the scaling action S = c N (J) on J3 (Os ) (dimR = 27, deg N = 3)" }, "caution": "This bare scaling identity does not determine the running of physical masses, which the source assigns to composite correlators.", "candidate_ids": [ "C2-144" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-058/", "content_sha256": "cd946e39739d36f86bdc0246fce623e829c919fc69c941d2e9efab74077eb62d", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-059", "entry_version": 9, "class": "CLAIM", "title": "The cubic coupling is relevant by the stated power count", "statement": "For a canonically normalised two-derivative kinetic term, the source's cubic coupling has mass dimension [c] = (6 − d)/2 and is relevant in d = 4.", "scope": { "carrier": "The cubic coupling in the source's norm-based model", "domain": "Engineering mass dimension and relevance, not an interacting mass prediction.", "group": null, "hypotheses": [ "Use the cubic interaction and power-counting convention stated in Remark 6.4." ], "physical_target": null, "quantifier": "The stated cubic model.", "real_form": "J3(Os)" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 209 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix I", "section": "§6, Remark 6.4(iii): cubic relevance", "pdf_page": 219, "quote": "the cubic coupling has mass dimension [c] = (6 − d)/2 for a canonically normalised two-derivative kinetic term (a premise, stated Rev32.9), relevant in d = 4 exactly as in ϕ3 theory" }, "caution": "Power-counting relevance does not compute physical mass running or derive a numerical confinement scale.", "candidate_ids": [ "C2-151" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-058" } ], "url": "/library-v2/LIB2-059/", "content_sha256": "b9920ce03128fd2bce63ffc028a14930a87f4c17da666c1c3b5611eda679bda4", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-060", "entry_version": 7, "class": "CLAIM", "title": "The solar-angle readout is conditional on ordering and the propagation interface", "statement": "Under the declared normal ordering, resolvent-ladder and propagation-interface premises, the solar-angle readout is tan θ12 = √3/ϕ².", "scope": { "carrier": "The registered PMNS solar-angle readout", "domain": "The physical solar-angle attachment, not the internal reciprocal-square identity.", "group": null, "hypotheses": [ "Normal ordering is assumed.", "The Structural Rd ladder is granted.", "Its identification with propagation eigenstates is an undeclared interface." ], "physical_target": "tan θ12", "quantifier": "The registered readout and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": "Derived-conditional", "pdf_page": 58 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 5", "section": "§2, Solar-angle expression", "pdf_page": 83, "quote": "√ PMNS 3 tan θ12 = 2, (PMNS solar angle — THEOREM) (1) ϕ" }, "caution": "The readout does not derive the mass ordering or the ladder-to-propagation-eigenstate interface.", "candidate_ids": [ "C2-004", "C2-058" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-046" }, { "type": "rests_on_premise", "target": "PRM-031" }, { "type": "rests_on_premise", "target": "PRM-033" } ], "url": "/library-v2/LIB2-060/", "content_sha256": "459b5449816dd6144d59755167971cd5b119659a396add56a1c1be8c84035de9", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-061", "entry_version": 12, "class": "CLAIM", "title": "The reactor-angle formula retains an unforced round-trip readout", "statement": "The retained reactor-angle formula is sin²θ13 = sin⁴(π/8); its round-trip T² squaring (the round-trip framing, exponent 2) is identified but not forced from first principles.", "scope": { "carrier": "The registered reactor-angle readout", "domain": "The retained structural formula, not a uniquely forced reactor-angle law.", "group": null, "hypotheses": [ "The round-trip framing T² and its squaring are used.", "The exponent choice remains an identity/heuristic selection." ], "physical_target": "sin²θ13", "quantifier": "The registered readout and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "Structural", "attachment": "NOT_PRINTED", "scorecard_tier_word": "Structural", "pdf_page": 58 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 5", "section": "§2, Reactor-angle expression", "pdf_page": 83, "quote": "sin2 θ13 = sin4 (π/8)" }, "caution": "Identifying the round-trip construction does not select its physical readout or promote the formula to a theorem.", "candidate_ids": [ "C2-006", "C2-060" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-061/", "content_sha256": "c250d9bd0df5977478f385144a46dae325cedf2682ca3660022890eedc7cf3fc", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-062", "entry_version": 8, "class": "CLAIM", "title": "The leptonic Dirac-phase readout remains conditional", "statement": "The retained leptonic phase readout is δCP = −2π/√5 = −160.997°, typed Derived-conditional (Rev29 re-tiering; the pre-Rev29 stamp was Theorem ⋆100), under the registered framing, normal ordering, ladder/interface premises and Dirac-neutrino benchmark.", "scope": { "carrier": "The registered V3-rotation phase readout", "domain": "Physical attachment of the orbit parameter, distinct from the internal generator results.", "group": null, "hypotheses": [ "The (1,3) framing sector is chosen.", "Normal ordering and the Structural Rd ladder are granted.", "The ladder-to-propagation-eigenstate interface is undeclared.", "Dirac neutrinos are the operative benchmark." ], "physical_target": "δCP", "quantifier": "The registered readout and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": "Derived-conditional", "pdf_page": 58 }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 5", "section": "§3, Phase expression", "pdf_page": 88, "quote": "δCP = −2π/ 5 = −160.997◦" }, "caution": "The internal rotation theorem does not by itself identify its orbit parameter with the measured Dirac phase.", "candidate_ids": [ "C2-007", "C2-061" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-051" }, { "type": "related_to", "target": "LIB2-052" } ], "url": "/library-v2/LIB2-062/", "content_sha256": "9470e83c20eafa3d81db428c74e88af5d9678489f979a0656a902319f01ae0de", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-063", "entry_version": 7, "class": "CLAIM", "title": "The framework-angle Route-B readout gives the corrected Cabibbo value", "statement": "The data-selected Route-B readout |Vus| = sin θ12/√6 gives 0.225256 when the framework solar angle is used.", "scope": { "carrier": "The Route-B Peirce first-row correspondence", "domain": "The corrected framework-angle readout, not its rounded-angle variant or measured-angle diagnostic.", "group": null, "hypotheses": [ "Use the framework solar angle rather than the measured NuFIT angle.", "Route B is selected against kaon data." ], "physical_target": "|Vus|", "quantifier": "The registered readout and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": "Loaded", "pdf_page": 51 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Paper 3", "section": "§2, Route-B readout", "pdf_page": 48, "quote": "The CKM first row is canonically fixed by the Peirce J12 block through Route B: PMNS sin θ12 |Vus | = √ ≈ 0.22526. (1) 6" }, "caution": "A derived block weight does not make the data-selected route a first-principles prediction.", "candidate_ids": [ "C2-009", "C2-062" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "depends_on", "target": "LIB2-060" }, { "type": "depends_on", "target": "LIB2-050" }, { "type": "compares_with", "target": "SL-11" }, { "type": "rests_on_premise", "target": "PRM-017" } ], "url": "/library-v2/LIB2-063/", "content_sha256": "b2fb35516ed4ae59dd411b6a67ce3a6f9508982f8cffc7d4c3190f242613ac4c", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-064", "entry_version": 7, "class": "CLAIM", "title": "The measured-angle Cabibbo diagnostic is a different readout object", "statement": "Feeding the measured NuFIT solar angle through the same first-row formula gives the separate diagnostic value |Vus| = 0.22687.", "scope": { "carrier": "The first-row formula evaluated using a measured solar angle", "domain": "A diagnostic using measured input, distinct from the framework-angle target.", "group": null, "hypotheses": [ "Insert the measured NuFIT solar angle, not the framework angle." ], "physical_target": "Measured-angle |Vus| diagnostic", "quantifier": "The registered readout and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 47 }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 3", "section": "§2, Measured-angle diagnostic", "pdf_page": 49, "quote": "Feeding the measured NuFIT solar angle through the same formula gives the separate diagnostic value 0.22687. Against the |Vus | comparator error alone that is +3.01σ; propagating the NuFIT θ12 error as well gives about +1.0σ (0.97–1.00, house recompute A1641), and only the propagated figure√ is a distance (Rev32.9)." }, "caution": "This measured-input diagnostic is not an independent prediction and does not upgrade the selected first-row route.", "candidate_ids": [ "C2-062" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-063" }, { "type": "compares_with", "target": "SL-11" } ], "url": "/library-v2/LIB2-064/", "content_sha256": "78a374c90aeb8ec16f2483b2e8a4d3d8bf01a612b8876c75dd153635907480c5", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-065", "entry_version": 9, "class": "CLAIM", "title": "The loaded first row determines its displayed Vud magnitude", "statement": "The retained first-row relation |Vud| = √(1 − |Vus|² − |Vub|²) gives the displayed value 0.97429 and inherits the first-row loading.", "scope": { "carrier": "The retained CKM first-row relation", "domain": "The displayed first-row completion, not an independently selected |Vud| formula.", "group": null, "hypotheses": [ "Use the loaded |Vus| and |Vub| entries in the stated unitarity relation." ], "physical_target": "|Vud|", "quantifier": "The registered readout and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": "Loaded", "pdf_page": 58 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "analytic", "availability": "shipped" } ], "primary_source": { "component": "Paper 3", "section": "§2, First-row unitarity readout", "pdf_page": 49, "quote": "first-row unitarity gives q |Vud | = 1 − |Vus |2 − |Vub |2 ≈ 0.97429. (3)" }, "caution": "The unitarity-derived value inherits the route choice and is not an independent confirmation of that choice.", "candidate_ids": [ "C2-008" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "depends_on", "target": "LIB2-063" }, { "type": "depends_on", "target": "LIB2-067" }, { "type": "compares_with", "target": "SL-14" }, { "type": "rests_on_premise", "target": "PRM-017" } ], "url": "/library-v2/LIB2-065/", "content_sha256": "4c771bc9d9eaccfac0ad2d9d2d9a102a41d70b2971f2851016cf2a25a657c8f4", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-066", "entry_version": 12, "class": "CLAIM", "title": "The Vcb formula retains its loaded physical attachment", "statement": "The retained formula |Vcb| = 1/(9√7) gives 0.041996; its physical attachment inherits the atmospheric registration and the independently unforced integer 9.", "scope": { "carrier": "The retained Peirce Vcb correspondence", "domain": "The structural formula with its loaded physical attachment.", "group": null, "hypotheses": [ "The physical atmospheric-octant registration is loaded.", "The integer 9 remains independently unforced." ], "physical_target": "|Vcb|", "quantifier": "The registered readout and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "Structural", "attachment": "Loaded-correspondence", "scorecard_tier_word": "Loaded-correspondence", "pdf_page": 51 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix B", "section": "§B.6, Vcb comparator row", "pdf_page": 162, "quote": "|Vcb | 1/(9 7) = 0.041996 0.0407 ± 0.0013 +1.00σ" }, "caution": "The exact formula does not select its integer or derive the physical atmospheric registration on which it depends.", "candidate_ids": [ "C2-010", "C2-063" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "depends_on", "target": "LIB2-002" }, { "type": "compares_with", "target": "SL-13" }, { "type": "rests_on_premise", "target": "PRM-013" } ], "url": "/library-v2/LIB2-066/", "content_sha256": "472e88f51fb664c366a33dcb54fef70dd450962c93a404f39c2ce96dd82fc49e", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-067", "entry_version": 8, "class": "CLAIM", "title": "The Vub hierarchy relation inherits the loaded Route-B chain", "statement": "The retained hierarchy relation |Vub| = |Vus||Vcb|/√6 gives 0.003862 within the loaded Route-B correspondence.", "scope": { "carrier": "The Route-B hierarchy relation", "domain": "The current displayed hierarchy value, not an independently selected CKM entry.", "group": null, "hypotheses": [ "Use the retained |Vus|, |Vcb| and first-row block weight.", "The route and inherited physical attachments remain loaded." ], "physical_target": "|Vub|", "quantifier": "The registered readout and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": "Loaded", "pdf_page": 58 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix B", "section": "§B.6, Vub hierarchy and displayed comparison", "pdf_page": 162, "quote": "|Vub | |Vus ||Vcb |/ 6 = 0.003862 0.00389 ± 0.00016 −0.18σ" }, "caution": "The hierarchy relation does not remove the route choice or supply an independent derivation of the full CKM matrix.", "candidate_ids": [ "C2-011", "C2-064" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "depends_on", "target": "LIB2-063" }, { "type": "depends_on", "target": "LIB2-066" }, { "type": "depends_on", "target": "LIB2-050" }, { "type": "compares_with", "target": "SL-12" }, { "type": "rests_on_premise", "target": "PRM-017" } ], "url": "/library-v2/LIB2-067/", "content_sha256": "d45d9b1aaa18bd779c9c09322a492974096547c5c4b3024586c47711cd47d53a", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-068", "entry_version": 7, "class": "CLAIM", "title": "The retained CKM-phase construction remains coincidence-class", "statement": "The retained construction δCKM = arctan√(3(ϕ + 5ϕ⁻⁵)) = 68.1297° remains Coincidence-class because the first-principles selection of G7 is absent.", "scope": { "carrier": "The retained G7-based CKM-angle construction", "domain": "The retained numeral and its current provenance, not a successful physical selection theorem.", "group": null, "hypotheses": [ "The chosen correction is 5ϕ⁻⁵.", "The selected Route-B matrix inputs are distinct from a derivation of G7." ], "physical_target": "δCKM", "quantifier": "The registered readout and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": "Coincidence-class", "pdf_page": 51 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 3", "section": "Candidate Construction 2.1, retained formula", "pdf_page": 53, "quote": "G7 = ϕ + 5ϕ−5 , q δCKM = arctan 3(ϕ + 5ϕ−5 ) = 68.1297◦" }, "caution": "Agreement of this numeral with data does not derive G7 or make the circular equal-shift step a selection law.", "candidate_ids": [ "C2-012", "C2-013", "C2-065" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-068/", "content_sha256": "38bb46b5e12a8c903be692d60a993186a9c17fd5f21a8e094f226c137e7558aa", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-069", "entry_version": 8, "class": "CLAIM", "title": "The retained CKM numeral has the printed global-phase comparison", "statement": "Against the named PDG global-fit Dirac phase, the suite assigns its retained CKM-phase numeral a central-value Gaussianized distance of +1.40σ in the primary radian representation (the degree presentation gives +1.41σ).", "scope": { "carrier": "The retained CKM numeral and the global-fit Dirac-phase comparator", "domain": "The source-reported numerical comparison.", "group": null, "hypotheses": [ "Use the named global-fit Dirac-phase comparator, not the direct UT-angle measurement.", "Copy the suite comparison convention and displayed distance." ], "physical_target": "Comparison with SL-19", "quantifier": "The registered readout and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 48 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 3", "section": "§2.1, Global-fit Dirac-phase comparator", "pdf_page": 50, "quote": "the global-fit Dirac phase δ = 1.154 ± 0.025 rad gives +1.40σ in that published representation, which is primary (R-29; the degree cells 66.12◦ ± 1.43◦ give +1.41σ)" }, "caution": "This comparator distance is not a profile likelihood or an independent validation of the G7 selection.", "candidate_ids": [ "C2-012", "C2-065" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-068" }, { "type": "compares_with", "target": "SL-19" } ], "url": "/library-v2/LIB2-069/", "content_sha256": "e24b27bdcbb984ccd94675dc3a72eefa4bda73d7b649674b465eccaf1018fde7", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-070", "entry_version": 7, "class": "CLAIM", "title": "The retained CKM numeral has a distinct direct-angle comparison", "statement": "Against the named direct unitarity-triangle angle γ, the suite assigns its retained CKM-phase numeral a central-value Gaussianized distance of +0.64σ.", "scope": { "carrier": "The retained CKM numeral and the direct UT-angle comparator", "domain": "A source-reported diagnostic comparison of distinct objects.", "group": null, "hypotheses": [ "Use the direct UT angle γ, not the global-fit Dirac phase.", "The stated Gaussianization uses the lower asymmetric comparator error." ], "physical_target": "Comparison with SL-20", "quantifier": "The registered readout and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 48 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 3", "section": "§2.1, Direct UT-angle comparator", "pdf_page": 50, "quote": "the direct UT-angle γ = 66.4+2.7 −2.8 gives +0.64σ (a numeral comparison: it scores the inserted δ = 68.1297◦ , while the assembled matrix’s own angle is γ(V ) = 68.0924◦ , +0.63σ; Rev32.9) — two distinct objects, each labelled where quoted." }, "caution": "This comparison does not identify γ with the Dirac phase or supply a derivation of the retained numeral.", "candidate_ids": [ "C2-013", "C2-065" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-068" }, { "type": "compares_with", "target": "SL-20" } ], "url": "/library-v2/LIB2-070/", "content_sha256": "413f602d7e40959acbdfdf23033a22722e7b2c7d5c4ea0077b389d39efc70bdc", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-071", "entry_version": 7, "class": "CLAIM", "title": "CKM unitarity holds by construction in the chosen parametrisation", "statement": "The CKM assembly satisfies all six unitarity relations identically because it uses the standard unitary parametrisation.", "scope": { "carrier": "The standard-form CKM assembly", "domain": "Algebraic unitarity of the assembly, not validation of the chosen entries.", "group": null, "hypotheses": [ "Insert the retained entries into the standard unitary parametrisation." ], "physical_target": "CKM matrix unitarity", "quantifier": "The registered readout and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 48 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "analytic", "availability": "shipped" } ], "primary_source": { "component": "Paper 3", "section": "§2.1, Unitarity of the standard parametrisation", "pdf_page": 50, "quote": "Because the matrix is built from the standard unitary parameterisation, all six unitarity relations hold identically." }, "caution": "Unitarity by construction is not an independent success and does not resolve the source’s CKM-angle inconsistency.", "candidate_ids": [ "C2-066" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-068" } ], "url": "/library-v2/LIB2-071/", "content_sha256": "666c94befec1d6b4da6a5980e87c9ff064bffa56e18c6012c7b87d018d167687", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-072", "entry_version": 8, "class": "CLAIM", "title": "The two CKM beta readouts remain internally inconsistent", "statement": "The suite reports βrecon = 23.44° from its standard CKM assembly, versus 22.5° from the separate half-angle construction, leaving an internal discrepancy of 0.94°.", "scope": { "carrier": "The standard CKM assembly and the independent half-angle construction", "domain": "The internal comparison printed in the suite, not a new fit or corrected reconstruction.", "group": null, "hypotheses": [ "Retain the two source-defined readout routes rather than selecting one against data." ], "physical_target": "CKM unitarity-triangle angle β", "quantifier": "The registered readout and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 53 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 3", "section": "§2.2, Internal consistency note", "pdf_page": 55, "quote": "A CKM matrix constructed from those four elements under the standard parametrisation gives βrecon = 23.44◦ , not 22.5◦ ." }, "caution": "Neither choosing the closer external comparison nor enforcing unitarity resolves the missing |Vtd| readout.", "candidate_ids": [ "C2-066" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-071" } ], "url": "/library-v2/LIB2-072/", "content_sha256": "f1761ddeb70033e47626a0513f1f163f6c00fa97818e9827bb08ae72a21e19f8", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-073", "entry_version": 8, "class": "CLAIM", "title": "The first-row weight is not a universal Peirce-block functor", "statement": "The naive S3 orbit-average map F(θ) = sin θ/√6 fails on |Vcb| by a factor 6.6, so the first-row weight is block-dependent rather than a universal functor.", "scope": { "carrier": "The proposed uniform map across the registered Peirce blocks", "domain": "Failure of this particular universal-weight map, not every block-dependent rule.", "group": null, "hypotheses": [ "Apply the stated first-row form to the Vcb block as in the source control." ], "physical_target": "Uniform mixing-weight transfer test", "quantifier": "The registered readout and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 59 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Paper 3", "section": "§5.2, Universal-weight control", "pdf_page": 63, "quote": "naive S3 -orbit- average functor F (θ) = sin θ/ 6 fails on |Vcb | by 6.6× (s1105: F (θ23 ) = sin θ23 / 6 = 0.270031 at sin2 θ23 =√7/16, which √ is 6.635 times the PDG comparator 0.0407 and 6.430 times the framework’s own 1/(9 7)), so 1/ 6 is a Peirce-block-dependent weight, not a functor;" }, "caution": "This control does not refute the first-row factorization or supply the missing block-dependent rule.", "candidate_ids": [ "C2-062" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-050" }, { "type": "related_to", "target": "LIB2-066" } ], "url": "/library-v2/LIB2-073/", "content_sha256": "10c91c533f2c9ed3f667b82b13d8e953dc964469fcf3965e59d30d2d18d469af", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-074", "entry_version": 7, "class": "CLAIM", "title": "PMNS unitarity is exact within its standard-form construction", "statement": "For the displayed standard-form PMNS matrix, U†U = I exactly by construction.", "scope": { "carrier": "The standard-form PMNS matrix of Eq. (20)", "domain": "Unitarity of the matrix construction, not the provenance of its angle inputs.", "group": null, "hypotheses": [ "Use the displayed trigonometric parametrisation of the retained PMNS entries." ], "physical_target": "PMNS matrix unitarity", "quantifier": "The registered readout and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "Proved", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 58 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "analytic", "availability": "shipped" } ], "primary_source": { "component": "Paper 3", "section": "§3.2, PMNS construction", "pdf_page": 56, "quote": "Unitarity is exact by construction: U † U = I." }, "caution": "Exact unitarity is not an independent falsification target and does not derive the input angles or their physical attachments.", "candidate_ids": [ "C2-066" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-060" }, { "type": "related_to", "target": "LIB2-061" }, { "type": "related_to", "target": "LIB2-062" }, { "type": "related_to", "target": "LIB2-002" } ], "url": "/library-v2/LIB2-074/", "content_sha256": "638b8c99d6e53841c3bf7ab46013c33e8a439f48c26d39ad2146d7a7587fe10c", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-075", "entry_version": 11, "class": "CLAIM", "title": "The uncorrected golden argument is closer on both named CKM comparisons", "statement": "The zero-correction control X = ϕ gives the printed angle 65.587°, closer than the retained G7 numeral to the global-fit phase (−0.37σ) and to the direct γ (−0.29σ).", "scope": { "carrier": "The X = ϕ control of the retained CKM-angle construction", "domain": "A published control, not a newly selected phase formula.", "group": null, "hypotheses": [ "Use the source’s zero-correction control and its two named comparator objects." ], "physical_target": "CKM-angle construction control", "quantifier": "The registered readout and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 51 }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Paper 3", "section": "Candidate Construction 2.1, Zero-correction control", "pdf_page": 54, "quote": "The uncorrected argument X = ϕ gives δ = arctan 3ϕ = 65.587◦ : −0.37σ against the global-fit 1.154 ± 0.025 rad and −0.29σ (the lower error, the side facing the value) against the direct γ = 66.4+2.7 ◦ −2.8 — closer than G7 on both comparators." }, "caution": "A closer control value is not a derived replacement phase law and does not justify another data-selected formula search.", "candidate_ids": [ "C2-065" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-068" }, { "type": "compares_with", "target": "SL-19" }, { "type": "compares_with", "target": "SL-20" } ], "url": "/library-v2/LIB2-075/", "content_sha256": "e89944bae7c1284652e3e374ebbadcd1b895ed7b10ed06e5035c4aa75fbc568d", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-076", "entry_version": 7, "class": "CLAIM", "title": "The enumerated compact embeddings fail the simultaneous-adjoint test", "statement": "For every one of the 21 enumerated faithful compact su(3) ⊕ su(2) classes, the restricted 56 lacks either the colour adjoint (8,1) or the weak adjoint (1,3).", "scope": { "carrier": "56 restricted through the enumerated faithful branchings of the su(8) fundamental", "domain": "The simultaneous-adjoint multiplicity test, not an independently certified domain-wide completeness result.", "group": "su(3) ⊕ su(2)", "hypotheses": [ "Use the 21 faithful classes enumerated in Appendix F §2.", "The carrier restricts as Λ²8 ⊕ Λ²8̄." ], "physical_target": null, "quantifier": "Every class in the printed finite census.", "real_form": "Compact su(3) ⊕ su(2) inside su(8)" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 175 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix F", "section": "§2, Proof step L4: adjoint multiplicities", "pdf_page": 181, "quote": "for every one of the 21 faithful classes, mult(8, 1) = 0 or mult(1, 3) = 0 in 56 ↓ ι = Λ2 8 ⊕ Λ2 8̄." }, "caution": "This record states the finite census; it neither independently verifies the broader all-frame theorem nor excludes noncompact real forms.", "candidate_ids": [ "C2-037" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-076/", "content_sha256": "a16cb954b5582ef38db9579c37914f1d04ba8316b11f6d31ff6d42efd7a7ba58", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-077", "entry_version": 10, "class": "CLAIM", "title": "The unitary matter-colour class has no image-compatible adjoint", "statement": "For the registered unitary matter-colour class, the invariant embedding-tensor space has dimension 140, and the union of its rowspaces has rank 125, its eight missing directions being exactly the su(3) adjoint.", "scope": { "carrier": "Inv_su(3),unitary(912) and its combined rowspace in the 133", "domain": "Rowspace orthogonality to the required colour adjoint.", "group": "su(3)", "hypotheses": [ "The unitary class is 8 = 3 ⊕ 5·1.", "Use the registered invariant embedding-tensor space and rowspace conventions." ], "physical_target": null, "quantifier": "The specified invariant space for this embedding class.", "real_form": "Compact unitary-class su(3) in su(8)" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 176 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix F", "section": "§3, Leg A: invariant-space dimension and rowspace rank", "pdf_page": 182, "quote": "dimension 140, matching the character prediction 140 = 2·15 (36⊕36)+2·55 (420⊕420) exactly (singular-value gap 8.9 × 1013 ). The union of the rowspaces of all invariant Θ has rank 125," }, "caution": "This embedding-class result does not identify a physical colour action elsewhere or supply a derivation of the compact Standard-Model boundary.", "candidate_ids": [ "C2-038" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-076" } ], "url": "/library-v2/LIB2-077/", "content_sha256": "b99eb22b4883307896b8e25a1799f9c3b86038bb8c1456719589fcb0c982ed95", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-078", "entry_version": 9, "class": "CLAIM", "title": "The frame-free real 56 has no invariant rank-one Higgs projector", "statement": "The bare real 56 admits no E7(7)-invariant rank-one projector; its invariant idempotents have ranks only 0 or 56.", "scope": { "carrier": "Real Freudenthal carrier F = R ⊕ R ⊕ J3(Os) ⊕ J3(Os)", "domain": "The unmarked real carrier, without a boundary selecting a line.", "group": "G0 = Aut(F,ω,Q)0", "hypotheses": [ "The full frame-free E7(7) action is retained.", "The source computes its real commutant as R·I." ], "physical_target": null, "quantifier": "Every invariant idempotent for the registered full action.", "real_form": "E7(7)" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 182 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "analytic", "availability": "shipped" }, { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix F", "section": "§7, Theorem 7.1: invariant projectors", "pdf_page": 188, "quote": "There is no G0 -invariant rank-one projector on the 56: the only invariant idempotents have rank 0 or 56." }, "caution": "The obstruction does not exclude a Higgs orientation supplied by a loaded boundary or selected by additional symmetry-breaking structure.", "candidate_ids": [ "C2-041" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-006" } ], "url": "/library-v2/LIB2-078/", "content_sha256": "02a37a6ebb0556d14d97e0e4b160dfcdc735e1115e658118c5c49ddcf270823a", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-079", "entry_version": 7, "class": "CLAIM", "title": "The scanned dyonic completion hosts a classical algebra-type shadow", "statement": "The scanned dyonic SO*(8) completion has a classical Minkowski vacuum with residual SO(6) × SO(2), hosting an su(3) ⊕ u(1) ⊕ u(1) shadow.", "scope": { "carrier": "The dyonic completion in the scanned potential family", "domain": "Classical existence and residual algebra type, not Standard-Model charge identification.", "group": "Residual su(3) ⊕ u(1) ⊕ u(1)", "hypotheses": [ "Use the scalar-origin construction and normalization in Appendix F §5.", "The scanned family is the electric SO(p,q)/CSO ladder, dyonic ω-rotated SO(8), and dyonic SO*(8)." ], "physical_target": null, "quantifier": "The named completion in the declared scanned family.", "real_form": "The SO*(8) completion and its compact residual SO(6) × SO(2)" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 179 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix F", "section": "§5.2, Dyonic completion at the origin", "pdf_page": 186, "quote": "is a genuine Minkowski vacuum (all seventy tadpoles zero) with residual SO(6) × SO(2), the published spectrum above, and the shadow hosted;" }, "caution": "This algebra-type shadow is not the Standard Model charge assignment, and the source makes no quantum-stability claim.", "candidate_ids": [ "C2-042" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-079/", "content_sha256": "a8d6a88ed3ba3d1d622d9687b76484156b077d84e3aeb232ce8494abd2398cf6", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-080", "entry_version": 8, "class": "CLAIM", "title": "The shadow family cannot reproduce the registered matter multiset", "statement": "The residual-class su(3) has only four singlets in the full 56, while the matter pattern requires nine inside a 27-plane; no point of the stated SO(6,2)/SO*(8) vacuum family carries that matter multiset.", "scope": { "carrier": "The full 56 under the residual-class su(3), compared with the required matter 27-plane", "domain": "The singlet-count obstruction, not a scan claiming all possible matter embeddings are absent.", "group": "Residual vector-class su(3)", "hypotheses": [ "Conjugation preserves the full-carrier representation content.", "The faithful su(3) class in the residual so(6) is the source-defined unique conjugacy class." ], "physical_target": null, "quantifier": "Every point in the stated vacuum family with that residual class.", "real_form": "The stated SO(6,2)/SO*(8) family" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 180 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix F", "section": "§5.2, Remark 5.2(b2): singlet count", "pdf_page": 186, "quote": "four su(3)-singlets in the entire 56, while the matter pattern requires nine inside a 27-plane." }, "caution": "This failure does not remove the classical shadow algebra; it rejects its identification with the required matter-charge pattern.", "candidate_ids": [ "C2-042" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-079" }, { "type": "related_to", "target": "LIB2-077" } ], "url": "/library-v2/LIB2-080/", "content_sha256": "5610dade052163bf1c2aef313bdaac60a2bca7f40aaac664d847451c5db40b3b", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-081", "entry_version": 7, "class": "CLAIM", "title": "The compact-completion result is conditional and enumeration-bounded", "statement": "Under the fixed sixteen-Weyl-fermion package, its hypercharges, the 10H-only scalar sector and the full-colour-plus-weak-action clause, the enumerated compact low-energy completions leave GSM up to U(1)B−L and global structure Γ.", "scope": { "carrier": "The fixed one-generation matter, charge and 10H-only scalar package", "domain": "Uniqueness of completion in the stated class, not gauge-group emergence.", "group": "GSM and the stated U(1)B−L extension", "hypotheses": [ "Fix the sixteen Weyl fermions and their registered YSM charges.", "Retain only the 10H scalar sector.", "Require gauging the full derived colour and weak action.", "Restrict the result to the exhausted foil family and adversary directions." ], "physical_target": null, "quantifier": "The printed finite completion inventory.", "real_form": "Compact reductive low-energy completions" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 178 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix F", "section": "§4, Theorem 4.1: fixed package", "pdf_page": 183, "quote": "Fix the derived one-generation package: exactly the sixteen Weyl fermions of the 16 with the derived hypercharges YSM , and the 10H -only scalar sector." }, "caution": "The result neither derives the input gauge group nor classifies every compact reductive group on the matter space.", "candidate_ids": [ "C2-043" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-081/", "content_sha256": "4eb29f47e8d42ba45c13b85c207f685b7c70815741db174bd2771ce905a4e04c", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-082", "entry_version": 8, "class": "CLAIM", "title": "The extra compact Cartan is the B−L charge direction", "statement": "For the registered completion filters, the Yukawa-neutrality and anomaly equations have, modulo the hypercharge direction, a one-dimensional extra-Cartan solution space, whose Higgs-doublet-neutral representative is (1,−1,−1,−3,3,3) = 3(B−L).", "scope": { "carrier": "Extra compact Cartan charges on the fixed matter package", "domain": "The unique surviving extra charge direction under the completion filters.", "group": "U(1)B−L", "hypotheses": [ "Use the fixed field dictionary, Yukawa-neutrality equations and anomaly system of Theorem 4.1." ], "physical_target": null, "quantifier": "The stated extra-Cartan solution space.", "real_form": "Compact low-energy completion" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 177 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix F", "section": "§4, Theorem 4.1(2): extra Cartan", "pdf_page": 183, "quote": "the extra compact Cartan is unique: modulo the existing hypercharge direction the extra solution space of the Yukawa- neutrality + anomaly system is one-dimensional, and in the Higgs-doublet-neutral representative it is spanned by (1, −1, −1, −3, 3, 3) = 3(B−L)" }, "caution": "The unique extra charge direction does not establish that its gauge boson exists or remove the empirical premise used to exclude it.", "candidate_ids": [ "C2-043" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-081" } ], "url": "/library-v2/LIB2-082/", "content_sha256": "be2416cf706a627c2f05ee5a39e5613b922994a92a1c9d03b4f6645203a3b9df", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-083", "entry_version": 7, "class": "CLAIM", "title": "The loaded local matter action has a correlated Z6 kernel", "statement": "On the loaded one-generation field dictionary, the correlated cyclic Z6 centre acts trivially on all sixteen states, yielding the faithful local action GSM/Z6.", "scope": { "carrier": "The sixteen-state one-generation field dictionary", "domain": "The trivially acting central subgroup, not the physical global bundle or line-operator choice.", "group": "GSM/Z6", "hypotheses": [ "Use Q = T3 + Y and the registered colour-triality and weak-duality assignments.", "The source evaluates 6Y + 2t + 3d ≡ 0 mod 6 on the whole package." ], "physical_target": null, "quantifier": "The local action on the specified matter states.", "real_form": "Compact GSM action" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 178 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "analytic", "availability": "shipped" } ], "primary_source": { "component": "Appendix F", "section": "§4.1, State-by-state centre check", "pdf_page": 185, "quote": "All sixteen states satisfy (3), so g generates a Z6 = Z3 × Z2 that acts trivially on the whole package;" }, "caution": "The faithful local quotient does not fix the physical global structure or the allowed line operators.", "candidate_ids": [ "C2-043" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-081" } ], "url": "/library-v2/LIB2-083/", "content_sha256": "19f447d3c8b4a11ab1c3bfdb084dd16a8f35a3c9537a22eb9bbcd46a669136e2", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-084", "entry_version": 8, "class": "CLAIM", "title": "The mirror ladder reproduces an NS/R parity pattern, not a spin structure", "statement": "The signed trace over the banked mirror/Lucas ladder reproduces the antiperiodic NS and periodic R parity pattern of the three-torus sector, with the Freudenthal bit playing the holonomy-sign role.", "scope": { "carrier": "The banked mirror/Lucas ladder and TS3 sector", "domain": "The parity pattern only, without a manifold, Spin bundle or physical holonomy construction.", "group": null, "hypotheses": [ "Use the registered signed trace, mirror ladder and Freudenthal bit." ], "physical_target": null, "quantifier": "The two levels of the banked finite-carrier check.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 269 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix P", "section": "§2, Theorem 2.3: signed-trace pattern", "pdf_page": 284, "quote": "The signed trace over the banked mirror (Lucas ±) ladder reproduces the antiperiodic (NS) / periodic (R) parity pattern of the three-torus sector TS3 , with the Freudenthal bit playing the role of the holonomy sign." }, "caution": "The parity pattern does not construct a spin structure, a principal Spin bundle or a lift of a frame bundle.", "candidate_ids": [ "C2-027" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-054" }, { "type": "cited_by_section", "target": "E-C05.2.claims-used" }, { "type": "cited_by_section", "target": "E-C05.2.prior-art" }, { "type": "cited_by_section", "target": "E-C05.2.sources-receipt" } ], "url": "/library-v2/LIB2-084/", "content_sha256": "1b546a35f70d5947c5925560f5873506e8c8621457238f6623ddd3d9e5c63f75", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-085", "entry_version": 7, "class": "CLAIM", "title": "The finite signatures require an internal structure or its equivalent proxy", "statement": "In the declared comparison class, bare four-dimensional spacetime data without the equivalent noncompact modulus, twisted internal bundle or grading variable cannot reproduce the three banked signatures.", "scope": { "carrier": "The three banked finite-carrier signatures and the declared four-dimensional comparison class", "domain": "The structure-necessity argument of Appendix P, not a spacetime-dimension measurement.", "group": null, "hypotheses": [ "No equivalent noncompact internal target modulus, twisted internal bundle or grading variable is supplied." ], "physical_target": null, "quantifier": "The declared comparison class, not four-dimensional theories with additional internal data.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 270 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix P", "section": "§2, Theorem 2.5: scope", "pdf_page": 285, "quote": "A four-dimensional model that lacks the equivalent internal structure — a noncompact internal modulus, an internal H 1 (−; Z2 ) / w1 ̸= 0 twisted bundle, and an internal grading circle — cannot reproduce the three banked signatures" }, "caution": "This argument does not force a fifth physical spacetime dimension; a four-dimensional model may import equivalent internal data.", "candidate_ids": [ "C2-026" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-055" }, { "type": "related_to", "target": "LIB2-084" } ], "url": "/library-v2/LIB2-085/", "content_sha256": "73d8562d18e2632d8f8863dff75e28ba7790650f9b4dc4ba87949c2978dc1c5d", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-086", "entry_version": 9, "class": "CLAIM", "title": "The reflected cone metric is colour-blind at tree level within each Peirce sector", "statement": "Within each registered Peirce sector, the octonionic colour components carry raw cone-Hessian eigenvalues of equal magnitude and opposite sign and one common eigenvalue in the reflected positive metric, so the reflected metric is colour-blind at tree level.", "scope": { "carrier": "The cone Hessian G on off-diagonal octonionic Peirce sectors", "domain": "The printed colour-isotropy statement, not an all-orders loop theorem.", "group": null, "hypotheses": [ "Use the cone Hessian and the working vacuum normalization of Appendix I §6." ], "physical_target": null, "quantifier": "Within each Peirce sector at tree level.", "real_form": "J3(Os)" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 209 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix I", "section": "§6, Remark 6.4(ii): colour isotropy", "pdf_page": 219, "quote": "Colour isotropy: within each Peirce sector the eight SU (3)-colour components of an off-diagonal octonionic entry carry G-eigenvalues of equal magnitude and opposite signs in the raw block (±2ξk , fourfold each — Remark 6.5); in the reflected positive metric they carry one common eigenvalue, so it is the reflected metric that is colour-blind at tree level" }, "caution": "Tree-level colour isotropy does not establish all-orders colour blindness or derive the compact colour group.", "candidate_ids": [ "C2-150" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-086/", "content_sha256": "5534b0987069510648791327c270f2346d700eccd16e831070bdd0d5e0f8cd0e", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-087", "entry_version": 8, "class": "CLAIM", "title": "Schur block structure does not force a zero triplet eigenvalue", "statement": "Schur symmetry supplies singlet–triplet block separation and scalar action λI on each irreducible triplet block, but does not force λ = 0.", "scope": { "carrier": "The representation-level Coleman–Weinberg Hessian at the registered vacuum", "domain": "The distinction between a permitted scalar block and a numerically vanishing eigenvalue.", "group": "The source’s G2 representation decomposition", "hypotheses": [ "Use the invariant block decomposition described in Appendix A §A.7.5." ], "physical_target": null, "quantifier": "What follows from the stated representation symmetry alone.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 146 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "analytic", "availability": "shipped" } ], "primary_source": { "component": "Appendix A", "section": "§A.7.5, Rev32.1 Schur correction", "pdf_page": 151, "quote": "Schur’s lemma ensures the block structure at the algebraic representation level — no singlet–triplet mixing, and scalar action λI on each irreducible triplet block; it does not by itself force λ = 0" }, "caution": "This correction neither reproduces the separate numerical zeros nor provides an all-orders protection theorem.", "candidate_ids": [ "C2-114" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-087/", "content_sha256": "bae9a64d75a3e506d792063cb269fbcc83de16a2005980ea8284e03ca9fde6fb", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-088", "entry_version": 9, "class": "CLAIM", "title": "Generic cross-block Yukawa loops are not yet covered by an Artin generator census", "statement": "Artin’s theorem establishes associativity when a diagram’s internal labels lie in a two-generated subalgebra; that containment is not established for generic cross-block Yukawa trilinears with three independent split-octonion entries.", "scope": { "carrier": "Internal algebra labels in generic cross-block Yukawa diagrams", "domain": "The internal-label containment question; external momentum conservation does not settle it.", "group": null, "hypotheses": [ "The ambient algebra is alternative.", "Artin’s conclusion applies where the diagram’s labels lie in a subalgebra generated by two elements." ], "physical_target": null, "quantifier": "The source-stated two-generator condition, not an unrestricted claim about all diagrams.", "real_form": "Split octonions Os" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 147 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix A", "section": "§A.7.8(ii), Conditional Artin application", "pdf_page": 153, "quote": "Where a diagram’s internal algebra labels lie in a subalgebra generated by two elements, associativity follows by Artin;" }, "caution": "Lack of established two-generator containment is not a proof that a particular loop correction is non-associative or nonzero.", "candidate_ids": [ "C2-114" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-088/", "content_sha256": "548f99fae7157b44f8e55dd8d9d8a9dc7f83bc9e6d227d44f0f7fdc21c310116", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-089", "entry_version": 7, "class": "CLAIM", "title": "The physical-to-boundary quadratic bridge space is one-dimensional", "statement": "For the registered physical/selector ten P and boundary ten B, dim HomKdyn(Sym²P,B) = 1.", "scope": { "carrier": "Physical/selector ten P and boundary ten B", "domain": "Quadratic symmetry-respecting maps from the physical/selector module to the boundary module.", "group": "Kdyn", "hypotheses": [ "Use the distinct registered P and B modules and the symmetric-square domain." ], "physical_target": null, "quantifier": "The specified equivariant Hom space.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 297 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix S", "section": "§9.3, Quadratic bridge census: P to B", "pdf_page": 313, "quote": "dim HomKdyn (Sym2 P, B) = 1" }, "caution": "The dimension count does not select a normalized physical bridge or identify the inequivalent linear modules.", "candidate_ids": [ "C2-120" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-016" }, { "type": "related_to", "target": "LIB2-017" } ], "url": "/library-v2/LIB2-089/", "content_sha256": "bd9ad61de54d61e42b4dbf4e2a4bf6d8aeb56825634feec590a0a80d27935de1", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-090", "entry_version": 7, "class": "CLAIM", "title": "The boundary-to-physical quadratic bridge space is two-dimensional", "statement": "For the registered boundary ten B and physical/selector ten P, dim HomKdyn(Sym²B,P) = 2.", "scope": { "carrier": "Boundary ten B and physical/selector ten P", "domain": "Quadratic symmetry-respecting maps from the boundary module to the physical/selector module.", "group": "Kdyn", "hypotheses": [ "Use the distinct registered B and P modules and the symmetric-square domain." ], "physical_target": null, "quantifier": "The specified equivariant Hom space.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 297 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix S", "section": "§9.3, Quadratic bridge census: B to P", "pdf_page": 313, "quote": "dim HomKdyn (Sym2 B, P ) = 2" }, "caution": "The available quadratic maps do not choose a copy or derive a physical boundary-to-selector response.", "candidate_ids": [ "C2-120" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-089" }, { "type": "related_to", "target": "LIB2-017" } ], "url": "/library-v2/LIB2-090/", "content_sha256": "f97365b198fe611ff6aba9cf72147f308a3f7be43ecad8d9a6cb7974f24eef69", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-091", "entry_version": 8, "class": "CLAIM", "title": "The declared invariant-connection class cannot cancel the holonomy obstruction", "statement": "Within the declared left-E7(7)-invariant principal SU(8) connection class, the forced canonical connection has full SU(8) holonomy escaping Ksel, so no connection in that class cancels the obstruction.", "scope": { "carrier": "Principal SU(8) connections on the registered symmetric-space carrier", "domain": "The holonomy obstruction, not a topological nonexistence of all reductions or connections.", "group": "Left E7(7) invariance; principal SU(8)", "hypotheses": [ "Use the declared invariant-connection class compatible with Ω and the loaded Ksel.", "The source’s Schur/Wang step leaves only the canonical symmetric-space connection." ], "physical_target": null, "quantifier": "Only the declared invariant-connection class.", "real_form": "E7(7)/SU(8)" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 183 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix F", "section": "§8, Declared connection class", "pdf_page": 189, "quote": "left-E7(7) -invariant principal SU (8) connections compatible with Ω and the loaded Ksel ." }, "caution": "This class-relative obstruction is not a topological no-section theorem and does not exclude a non-equivariant preserving connection.", "candidate_ids": [ "C2-105" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-021" }, { "type": "related_to", "target": "LIB2-045" } ], "url": "/library-v2/LIB2-091/", "content_sha256": "05b6eedb6981f7f463162b3fe1bfa6152878cbe6c8d3ebd84757d37d85ec09fa", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-092", "entry_version": 8, "class": "CLAIM", "title": "Near-137 golden formulas carry no selection evidence under the stated density test", "statement": "Under the registered Beatty/Wythoff admissibility count, golden scale-free ratios densely populate the neighbourhood of 137, so a near-137 hit carries no selective information.", "scope": { "carrier": "Golden scale-free ratios in the registered admissibility count", "domain": "The tested near-137 formula family, not a probability law over every possible theory.", "group": null, "hypotheses": [ "Use the controlled density discipline described in Appendix N, Leg 2." ], "physical_target": null, "quantifier": "The declared source class only.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 252 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix N", "section": "§1.2, Leg 2: golden numerology density", "pdf_page": 264, "quote": "Scale-free ratios built from φ populate the neighbourhood of 137 densely; under a controlled density discipline (a Beatty/Wythoff admissibility count), a near-137 hit is expected by chance and therefore carries no selective information." }, "caution": "This density result does not derive the electromagnetic coupling or assign a global significance to arbitrary formulas.", "candidate_ids": [ "C2-137" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-092/", "content_sha256": "73d33b921bdc8205833fb0b0c5bb8cf1eef52904d400c7b7eadad81dbbefd492", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-093", "entry_version": 9, "class": "CLAIM", "title": "Golden-torus robustness does not select the coupling in the tested dissipative model", "statement": "In the registered Frenkel–Kontorova/Peierls–Nabarro comparison, an energy or dissipative principle mode-locks to rationals, while the golden value slides freely below the Aubry threshold Kc = 0.971635 and pins at and through it.", "scope": { "carrier": "The golden-torus robustness and dissipative mode-locking comparison", "domain": "Robustness versus coupling selection in these registered models.", "group": null, "hypotheses": [ "Use the standard-map and Frenkel–Kontorova/Peierls–Nabarro settings named in Appendix N, Leg 3." ], "physical_target": null, "quantifier": "The declared source class only.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 252 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix N", "section": "§1.3, Leg 3: mode-locking comparison", "pdf_page": 264, "quote": "in a Frenkel–Kontorova / Peierls–Nabarro setting an energy/dissipative principle mode-locks to rationals; the golden value slides freely below the Aubry threshold Kc = 0.971635 and pins at and through it" }, "caution": "The comparison does not exclude all stabilization mechanisms; it does not turn robustness into a derivation of a coupling.", "candidate_ids": [ "C2-137" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-092" } ], "url": "/library-v2/LIB2-093/", "content_sha256": "0a05b391eddd0b7d29b6d7718711be84fcf82a4ce0b12bf33d4e1b6879f6e4a9", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-094", "entry_version": 8, "class": "CLAIM", "title": "A continuous Reynolds offset does not supply the discrete rung selector", "statement": "For the registered resolvent depth ladder, a continuous Reynolds-offset spurion can shift positions but cannot leap the discrete integer steps; the occupation selector remains a winding datum.", "scope": { "carrier": "The resolvent depth ladder and continuous Reynolds offset", "domain": "The distinction between shifting a ladder position and selecting an occupied integer rung.", "group": null, "hypotheses": [ "Use the registered resolvent ladder and its integer depth labels." ], "physical_target": null, "quantifier": "The declared source class only.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 252 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix N", "section": "§1.4, Leg 4: continuous offset and winding selection", "pdf_page": 265, "quote": "can shift positions on the ladder but cannot leap its discrete integer steps; therefore the integer selector (the occupation of Appendix M, in Paper 0’s bound sense: which integer rungs are occupied; Rev32.9, A1647 U1) is a discrete topological (winding) datum, not a continuous correction." }, "caution": "The distinction does not construct the winding selector or remove the premises of the conditional occupation result.", "candidate_ids": [ "C2-068" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-029" } ], "url": "/library-v2/LIB2-094/", "content_sha256": "04f7f477b5952e599d90e3e4cfb198962b60e899c9c860c2b64d8b824609e96e", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-095", "entry_version": 9, "class": "CLAIM", "title": "The registered radial vacuum-decay route supplies no scale for alpha", "statement": "For the registered normalized radial potential, there is no lower vacuum to tunnel to and, under the stated premises, no nontrivial decay bounce; this proposed decay route supplies no dynamical scale to pin α.", "scope": { "carrier": "The normalized radial potential VN(r) of Appendix N, Leg 5", "domain": "The tested radial Coleman-decay route, not a general quantum-stability statement about the full vacuum.", "group": null, "hypotheses": [ "Use the radial potential VN(r) = Λ⁴(e⁻²ʳ + 2eʳ − 3) and its stated minimum at r = 0." ], "physical_target": null, "quantifier": "The declared source class only.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 253 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix N", "section": "§1.5, Leg 5: absent tunnelling solution", "pdf_page": 265, "quote": "so there is nowhere lower to tunnel to and the Euclidean equation of motion has only the trivial solution: no nontrivial decay bounce exists in this radial problem (positive canonical kinetic term; a regular finite-action solution approaching r = 0; vanishing boundary term), and the trivial vacuum has zero action relative to itself" }, "caution": "The radial result neither establishes full quantum stability nor turns classical geodesic reflection into a coupling-generating decay.", "candidate_ids": [ "C2-175" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-095/", "content_sha256": "f29b5603bc812ef7a5d0ce87aeb9f0e00ae84ae79341d9496510c2297552fc25", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-096", "entry_version": 7, "class": "CLAIM", "title": "The available compact part is too small for compact colour", "statement": "In the split-real loaded subimage of Appendix N, maximal compact dimension 6 is smaller than dim su(3) = 8, obstructing a compact-colour embedding in that available compact part.", "scope": { "carrier": "The compact part available to the loaded split-octonion subimage", "domain": "The compact-colour real-form obstruction, distinct from the embedding-tensor charge wall.", "group": "Compact su(3)", "hypotheses": [ "Retain the split real-form setting and the maximal compact part specified in Appendix N, Part N.B." ], "physical_target": null, "quantifier": "The declared source class only.", "real_form": "Split g2(2) setting of Appendix N, Part N.B" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 253 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix N", "section": "§2, Proposition 2.1: compact-colour obstruction", "pdf_page": 266, "quote": "The compact colour algebra su(3) (dimension 8) cannot embed in the compact part available to the loaded subimage, whose maximal compact dimension is 6 < 8." }, "caution": "This real-form obstruction does not ban compact colour in other carriers or derive the choice of the physical real form.", "candidate_ids": [ "C2-038" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-077" }, { "type": "cited_by_section", "target": "E-C01.2.claims-used" }, { "type": "cited_by_section", "target": "E-C01.2.derivation" }, { "type": "cited_by_section", "target": "E-C01.2.prior-art" } ], "url": "/library-v2/LIB2-096/", "content_sha256": "7c46f5d037275bc74cbc529ac853d31303631163d743c033d94810234ebc074a", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-097", "entry_version": 8, "class": "CLAIM", "title": "The tested translators do not extract a common line per clock weight", "statement": "The three registered translator velocities pick different lines in the weight-graded carrier, so their test does not extract the one-state-per-weight truncation.", "scope": { "carrier": "The weight-graded 56 and the three registered translator velocities", "domain": "Cross-translator agreement, not the nonzero and ladder-closure gates.", "group": null, "hypotheses": [ "Use the translators Rk for k = 3,4,5 and the frozen gates of s709." ], "physical_target": null, "quantifier": "The declared source class only.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 254 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix N", "section": "§2, Carrier truncation: cross-translator outcome", "pdf_page": 266, "quote": "The three translators pick different lines in the 27." }, "caution": "The nonzero and ladder-closure gates pass; this result rejects only the tested extraction of a shared line.", "candidate_ids": [ "C2-038" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-096" } ], "url": "/library-v2/LIB2-097/", "content_sha256": "9f0b562b94e099ebd4e018a542af78dacc422ba539298f50f424142d78fb587d", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-098", "entry_version": 8, "class": "CLAIM", "title": "The bare Freudenthal carrier does not select the electroweak framing package", "statement": "The bare Freudenthal system does not select a frame-free package DH = (PH,Nann,qH): its Higgs line is unavailable invariantly, its winding level lacks a frame-free basepoint, and its quadratic refinement remains a torsor.", "scope": { "carrier": "The framed-depth package DH = (PH,Nann,qH) on the bare Freudenthal system", "domain": "The joint framing package required for the electroweak scale registration.", "group": "G0 = E7(7)", "hypotheses": [ "Retain the full frame-free automorphism group G0 = E7(7).", "No Higgs-line, level-basepoint or quadratic-refinement marking is supplied." ], "physical_target": null, "quantifier": "The declared source class only.", "real_form": "Split Freudenthal system" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 254 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix N", "section": "§3, Proposition 3.1: package obstruction", "pdf_page": 267, "quote": "No frame-free package DH exists on the bare Freudenthal system F = R ⊕ R ⊕ J3 (Os ) ⊕ J3 (Os ) under its automorphism group G0 = E7(7) ." }, "caution": "The obstruction leaves the marked-carrier registration conditional; it does not forbid supplying the framing as loaded input.", "candidate_ids": [ "C2-041" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-078" } ], "url": "/library-v2/LIB2-098/", "content_sha256": "eedb503e8dd8c7c9bc0a412c447f137f7a68c4431fbe077e3154624153718953", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-099", "entry_version": 8, "class": "CLAIM", "title": "The orphan-doublet ruling is class-relative and the finite subgate is not the full row", "statement": "In the declared frozen-carrier class the orphan doublet fails as sole parent datum; global Row 1 remains open for genuinely external categories, the conditional Row-2 subgate passes, and the original full Row 2 remains open.", "scope": { "carrier": "The orphan doublet and the two Plan-v2 rows", "domain": "The source’s four-part dual ruling; a finite subgate does not establish a continuum trajectory.", "group": null, "hypotheses": [ "The local exclusion is restricted to the frozen-V56 BeatFlip class named before target loading.", "Genuinely external categories not factoring through the orphan-image class are outside that exclusion." ], "physical_target": null, "quantifier": "The declared source class only.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 255 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix N", "section": "§4, Local Row-1 exclusion", "pdf_page": 268, "quote": "Row 1 is KILLED — but only as a sole parent datum, and only inside the declared class." }, "caution": "The local exclusion does not reach genuinely external categories, and a passing finite subgate is not a continuum result.", "candidate_ids": [ "C2-105" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-021" }, { "type": "related_to", "target": "LIB2-045" } ], "url": "/library-v2/LIB2-099/", "content_sha256": "a5a3dbe082c154ad1462bd8fabefdec91dcd7eb6c898055e94568134c93a794a", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-100", "entry_version": 8, "class": "CLAIM", "title": "The registered octant construction does not exclude the mirror registration", "statement": "The chirality torsor {−1,+1} and octant torsor {7/16,9/16} admit two equivariant identifications, and no registered action term, operator, intertwiner or readout excludes the countermap.", "scope": { "carrier": "The chirality and atmospheric-octant torsors", "domain": "Nonselection of the physical registration, distinct from the internal mismatch identity.", "group": "Z2-equivariant identifications", "hypotheses": [ "Use the registered odd chirality carrier and equivariant torsor identifications of s1156." ], "physical_target": null, "quantifier": "The two registered torsor identifications and the banked selecting objects.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 257 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix N", "section": "§6, Octant-registration fence", "pdf_page": 269, "quote": "the chirality torsor {−1, +1} and the octant torsor {7/16, 9/16} admit exactly two Z2 -equivariant identifications (s1156: −1 7→ 7/16 and its mirror), and no registered action term, operator, intertwiner or readout map excludes the countermap." }, "caution": "The nonselection result does not refute the internal mismatch identity or derive a theory-fixed odd coupling sign.", "candidate_ids": [ "C2-005", "C2-059" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-356" }, { "type": "related_to", "target": "LIB2-002" } ], "url": "/library-v2/LIB2-100/", "content_sha256": "c510a36d7ca1710840846b75a52048dda08956d2687080c8f6257baf11c84b7d", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-101", "entry_version": 7, "class": "CLAIM", "title": "The registered ladder and phase census contains no selected complex rung ratio", "statement": "The census of 29 ladder/family rows against 39 phase/rotation rows registers no phase-bearing ratio q = ϕ⁻¹ exp(iα) selected by one source law fixing both the real rung and a nonzero angle.", "scope": { "carrier": "The shipped ladder/family and phase/rotation rows", "domain": "The shipped component census, not a universal impossibility theorem for future source laws.", "group": null, "hypotheses": [ "The required object is QL = SL exp(αJL), with JL² = −I and [JL,SL] = 0.", "One source law must fix both the real rung step and a nonzero α; installing a complex structure or choosing an angle does not qualify." ], "physical_target": null, "quantifier": "The declared source class only.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 257 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix N", "section": "§6, Complex-ratio ladder census", "pdf_page": 270, "quote": "a census of 29 ladder/family rows against 39 phase/rotation rows across the shipped components registers no q = ϕ−1 eiα ;" }, "caution": "Commuting scaling and phase candidates do not by themselves select a nonzero phase or its physical attachment.", "candidate_ids": [ "C2-104" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-015" } ], "url": "/library-v2/LIB2-101/", "content_sha256": "133d4a7f44ee54dd2fb078f2851f66935f84df5dc06864be8bbd67e0e41b7194", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-102", "entry_version": 8, "class": "CLAIM", "title": "The registered Jordan-scaling centralizer has the printed dimension and signature", "statement": "The registered scaling centralizer C(Lvac) ⊂ e6(6) has dimension 30, displayed signature (18,12,0), and centre dimension 2.", "scope": { "carrier": "The registered 27-carrier and scaling operator Lvac", "domain": "The single registered Jordan-scaling centralizer.", "group": null, "hypotheses": [ "Use the source’s centralizer C(Lvac) inside e6(6).", "Retain the displayed signature convention; no different bilinear form or real-form label is inferred." ], "physical_target": null, "quantifier": "The declared source class only.", "real_form": "e6(6)" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 257 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix N", "section": "§6, Jordan-scaling centralizer census", "pdf_page": 270, "quote": "C(Lvac ) ⊂ e6(6) has dimension/signature/centre 30, (18, 12, 0), 2," }, "caution": "A compact subalgebra inside the centralizer does not select a complex structure, angle or physical rung-to-phase map.", "candidate_ids": [ "C2-104" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-101" } ], "url": "/library-v2/LIB2-102/", "content_sha256": "29026f0207a086c3a77eade2c2e284064408a6679d3501a9eb78240bd5373a3e", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-103", "entry_version": 8, "class": "CLAIM", "title": "The registered grading centralizer has the printed dimension and signature", "statement": "The registered grading centralizer C(H) ⊂ e7(7) has dimension 79, displayed signature (43,36,0), and centre dimension 1.", "scope": { "carrier": "The registered 56-carrier and grading H", "domain": "The centralizer of H, not of the separate Appendix-H compact generator K.", "group": null, "hypotheses": [ "Use the source’s C(H) centralizer inside e7(7).", "Retain the source’s displayed signature convention." ], "physical_target": null, "quantifier": "The declared source class only.", "real_form": "e7(7)" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 257 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix N", "section": "§6, Grading centralizer census", "pdf_page": 270, "quote": "C(H) ⊂ e7(7) has 79, (43, 36, 0), 1." }, "caution": "The presence of compact directions does not fix their angles, and the Appendix-H K is not a member of this centralizer.", "candidate_ids": [ "C2-104" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-101" }, { "type": "related_to", "target": "LIB2-102" } ], "url": "/library-v2/LIB2-103/", "content_sha256": "16c6d274c91eb17605d2d3871cc18dd769fc6747bbbeab1ab3689386e7384ae9", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-104", "entry_version": 7, "class": "CLAIM", "title": "The bare quartic is not stationary at the registered golden boundary point", "statement": "At the registered split-real golden boundary point z0, dI4(z0) ≠ 0, so the bare quartic cannot by itself select that point as a stationary vacuum.", "scope": { "carrier": "The bare quartic I4 at the registered golden boundary point z0", "domain": "Stationarity of the bare quartic only, not the constrained potentials treated elsewhere.", "group": null, "hypotheses": [ "Retain the declared split real form.", "Appendix Q assigns its statements conditional tier on the κphys candidate mechanism." ], "physical_target": null, "quantifier": "The declared source class only.", "real_form": "Declared split real form" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 277 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix Q", "section": "§3(i), Bare-quartic gradient", "pdf_page": 292, "quote": "z0 is not a critical point of the bare quartic. Direct computation gives dI4 (z0 ) ̸= 0," }, "caution": "Nonstationarity of the bare quartic does not contradict stationarity of a separately constrained or sourced action.", "candidate_ids": [ "C2-042" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-079" } ], "url": "/library-v2/LIB2-104/", "content_sha256": "977583e35e0fda3585fa223ff24315a5992f395b40eec756cdd0d716819ece5b", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-105", "entry_version": 13, "class": "CLAIM", "title": "The stated split-G2 involution family yields no positive equivariant polarization", "statement": "In the declared split-G2 family, the four equivariant involutions J = sP1 + tPIm give signatures (4,4), (5,3), (3,5) and (4,4); none is positive.", "scope": { "carrier": "Equivariant polarizing involutions on the split-octonion carrier", "domain": "The enumerated equivariant involution family, not arbitrary polarizations or other real forms.", "group": "Der(Os)-equivariance", "hypotheses": [ "The commutant of Der(Os) in End(Os) has the source-reported dimension two.", "The split norm on Im Os has signature (3,4).", "Use involutions of the stated form J = sP1 + tPIm; Appendix Q retains its κphys conditional tier." ], "physical_target": null, "quantifier": "The declared source class only.", "real_form": "Split G2 / split octonions" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 277 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix Q", "section": "§3(ii), Polarization obstruction", "pdf_page": 292, "quote": "No positive equivariant polarization exists in the split-G2 family." }, "caution": "The exclusion is confined to the stated equivariant split-real involutions; it does not rule out polarizations using additional data.", "candidate_ids": [ "C2-042" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-104" }, { "type": "related_to", "target": "LIB2-096" }, { "type": "rests_on_premise", "target": "PRM-002" } ], "url": "/library-v2/LIB2-105/", "content_sha256": "d9ecd47fc9bbcf6b5b912df6090000a2edbb2ec04650549f2c1e0e1e0a7cec52", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-106", "entry_version": 8, "class": "CLAIM", "title": "The exact single-chi additive ratio completion fails on the registered support", "statement": "The exact single-χ completion r = χ²/(ϕ²ᴺ + χ²) fails on every bijection of the occupancy support {0,3,11,17}, with 0/24 admissible bijections.", "scope": { "carrier": "The single-χ additive mass-ratio completion on the registered occupancy depths", "domain": "The exact single-χ ratio class; the ordered depth skeleton and approximate shape are separate.", "group": null, "hypotheses": [ "Use one universal χ in the ratio formula stated in Appendix O, Remark 5.2.", "Test the charged-lepton and up-type ratios on the specified occupancy support." ], "physical_target": null, "quantifier": "Every bijection of the registered support in the stated ratio test.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": "REFUTED", "pdf_page": 7 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix O", "section": "§5, Remark 5.2: single-chi test", "pdf_page": 276, "quote": "an exact single-χ closure fails on every bijection of the support (0/24 admissible;" }, "caution": "This exact-class failure leaves the depth skeleton and approximate shape intact and is not a universal two-parameter no-go.", "candidate_ids": [ "C2-055" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-029" } ], "url": "/library-v2/LIB2-106/", "content_sha256": "8d0d1ff48e7bf51c70a742c2f79e4497b62e152c99fa63588f6294f67b2cb1b2", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-107", "entry_version": 8, "class": "CLAIM", "title": "The signed metric-weighted residue cannot supply the positive seven count", "statement": "For a subcollection of registered g-orthonormal Im Os channels, the signed residue equals the positive-minus-negative channel count and lies in [−4,+3], excluding 7 as that metric-weighted residue.", "scope": { "carrier": "Subcollections of g-orthonormal imaginary split-octonion channels", "domain": "The specific metric-weighted residue route; unweighted index and other physical realizations are different objects.", "group": null, "hypotheses": [ "The imaginary split-octonion metric has signature (3,4).", "Use the signed channel-count residue of Lemma 8.3, not arbitrary independent channel weights." ], "physical_target": null, "quantifier": "Any subcollection of the registered g-orthonormal channels.", "real_form": "Split octonions Os" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 212 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix I", "section": "§8, Lemma 8.3: signed-residue range", "pdf_page": 222, "quote": "The signed residue over any sub- collection of g-orthonormal channels equals (#positive − #negative) and therefore lies in the closed range [−4, +3]" }, "caution": "This bound does not refute the finite trace/index theorem or exclude every non-residue physical realization of the ratio.", "candidate_ids": [ "C2-044", "C2-054" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-053" }, { "type": "cited_by_section", "target": "E-C08.2.claims-used" }, { "type": "cited_by_section", "target": "E-C08.2.definitions-conventions" }, { "type": "cited_by_section", "target": "E-C08.2.prior-art" } ], "url": "/library-v2/LIB2-107/", "content_sha256": "8a6f2f9f43e7aec6849f386ba6274e0802fb0411c6903473689330c122319b14", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-108", "entry_version": 8, "class": "CLAIM", "title": "The explicit B-map fixes a loaded one-generation field dictionary", "statement": "Under the explicit B-map and compact field dictionary, the one-generation quark and lepton placements and all sixteen hypercharges are fixed.", "scope": { "carrier": "The one-generation Peirce-block field dictionary", "domain": "The loaded one-generation dictionary, not a derivation of the compact frame or generation count.", "group": null, "hypotheses": [ "Use the explicit B-map and the compact Standard-Model embedding.", "The Dirac-neutrino extension is assumed." ], "physical_target": null, "quantifier": "The registered construction and its stated hypotheses.", "real_form": "Split Jordan carrier with a loaded compact gauge dictionary" }, "source_labels_as_printed": { "math_status": "Proved", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 27 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 1", "section": "§6, Status under the explicit B-map", "pdf_page": 29, "quote": "Status under B: all one-generation quark and lepton placements and all sixteen hypercharges are PROVED under the explicit B-map (A689)." }, "caution": "This one-generation dictionary does not select the compact gauge boundary or construct the explicit three-generation embedding.", "candidate_ids": [ "C2-040" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "rests_on_premise", "target": "PRM-012" }, { "type": "rests_on_premise", "target": "PRM-011" }, { "type": "rests_on_premise", "target": "PRM-032" } ], "url": "/library-v2/LIB2-108/", "content_sha256": "9e9d82c91b1607cf73712c8934c6ac90fd1df8315394b27abd5a4d160bb3f0e3", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-109", "entry_version": 10, "class": "CLAIM", "title": "The loaded one-generation dictionary cancels the stated anomalies", "statement": "Under the explicit B + SU(5) embedding, the one-generation Standard-Model gauge anomaly sums vanish and the mixed U(1)-gravitational anomaly sum vanishes, and the Witten SU(2) anomaly is absent.", "scope": { "carrier": "The loaded one-generation chiral matter and hypercharges", "domain": "Anomaly cancellation for the specified field dictionary.", "group": "Compact SU(3)c × SU(2)L × U(1)Y", "hypotheses": [ "Use the explicit B + SU(5) embedding and the left-handed Weyl convention.", "The compact Standard-Model action is fixed." ], "physical_target": null, "quantifier": "The registered construction and its stated hypotheses.", "real_form": null }, "source_labels_as_printed": { "math_status": "Proved", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 29 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Paper 1", "section": "§8, Local anomaly sums", "pdf_page": 30, "quote": "In the left-handed Weyl convention the local anomaly coefficients all vanish (kernel-verified, cross-checked in house, A696):" }, "caution": "Anomaly cancellation does not select the compact embedding or determine the number of complete generations.", "candidate_ids": [ "C2-040" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "depends_on", "target": "LIB2-108" } ], "url": "/library-v2/LIB2-109/", "content_sha256": "b7deadf09408e662562d4e8d27fafff66b490167b79fed894f7b09fe1b727c5e", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-110", "entry_version": 8, "class": "CLAIM", "title": "The loaded split-octonion cubic has a nonzero invariant trilinear", "statement": "The split-octonion trilinear T(c,b,a) = Re(c·(b·a)) is nonzero and invariant under Der(Os) in the registered loaded cubic channel.", "scope": { "carrier": "The trilinear on the loaded Albert cubic channel", "domain": "Existence and invariance of the trilinear, not uniqueness of all invariant trilinears.", "group": "Der(Os) = g2(2)", "hypotheses": [ "Use the split-octonion product and the source's ordered trilinear channel." ], "physical_target": null, "quantifier": "The registered construction and its stated hypotheses.", "real_form": "Split octonions and J3(Os)" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 228 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix K", "section": "§2.1, Theorem 2.1: trilinear", "pdf_page": 239, "quote": "T (c, b, a) = Re c · (b · a)" }, "caution": "The existence of this invariant does not establish its uniqueness or determine physical Yukawa coefficients.", "candidate_ids": [ "C2-052" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-110/", "content_sha256": "66c7534e7903234eac5d74531e82254d85c9175413a42408935840b4e526c822", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-111", "entry_version": 7, "class": "CLAIM", "title": "The loaded hypercharge projection gives the four Yukawa tensors", "statement": "The loaded U(1)Y Reynolds projection of the registered trilinear equals the four one-generation Yukawa tensors {Q uᶜ H, L νᶜ H, Q dᶜ Hᶜ, L eᶜ Hᶜ}.", "scope": { "carrier": "The raw trilinear and its loaded hypercharge-zero projection", "domain": "Tensor structure on the allowed channel set, not a coefficient hierarchy.", "group": "Loaded U(1)Y", "hypotheses": [ "Use the explicit one-generation dictionary and the loaded U(1)Y action.", "Apply the registered Reynolds projector PY=0." ], "physical_target": null, "quantifier": "The registered construction and its stated hypotheses.", "real_form": "Loaded split Albert cubic" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 229 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix K", "section": "§1, Positive Yukawa statement", "pdf_page": 238, "quote": "projects onto exactly the four SM Yukawa tensors {Q uc H, L ν c H, Q dc H c , L ec H c }, with a single democratic common normalization (1, 1, 1, 1)." }, "caution": "The projected tensor structure does not select the loaded hypercharge action or split the four coefficient values.", "candidate_ids": [ "C2-053" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-108" }, { "type": "related_to", "target": "LIB2-110" } ], "url": "/library-v2/LIB2-111/", "content_sha256": "f0d63fc168a17d9f90e3d97063cc4c7eeafb108fba1bde68e2f6ccb4ffb7319f", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-112", "entry_version": 8, "class": "CLAIM", "title": "Exactly half of the raw trilinear norm lies in forbidden mirror sectors", "statement": "Exactly half of the raw trilinear squared norm lies in total-hypercharge ±1 mirror sectors, and the loaded U(1)Y Reynolds projector removes that leakage.", "scope": { "carrier": "The raw and hypercharge-projected split-octonion trilinears", "domain": "The forbidden-mirror component norm and its removal.", "group": "Loaded U(1)Y", "hypotheses": [ "Use the loaded hypercharge assignments and the squared component norm of the A1048 census." ], "physical_target": null, "quantifier": "The registered construction and its stated hypotheses.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 229 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix K", "section": "§3.2, Half-norm mirror leakage", "pdf_page": 240, "quote": "the raw octonionic trilinear τ carries exactly half of its squared norm as Y = ±1 “forbidden mirror” leakage:" }, "caution": "Removing forbidden mirror components does not derive the hypercharge loading or create a non-democratic hierarchy.", "candidate_ids": [ "C2-047" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-111" } ], "url": "/library-v2/LIB2-112/", "content_sha256": "e5920ca55686be5adda756d319d95a24ff98e3fd9bb915360a14ca931aa28efb", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-113", "entry_version": 9, "class": "CLAIM", "title": "Reynolds preservation of the registered raw coefficient ray", "statement": "The loaded U(1)Y Reynolds average PY=0 is the identity on the span of the four displayed Yukawa channel tensors, each of total hypercharge 0, so it retains every coefficient vector on that span without reweighting — in particular the common ray (1,1,1,1) of the registered raw tensor. This is preservation, not selection: nothing in the projection excludes an unequal quartet on the same span.", "scope": { "carrier": "The span of the four displayed Yukawa channel tensors, all of total hypercharge 0 (s1171 T1)", "domain": "UV/matching coefficients, not low-energy equality.", "group": "U(1)Y (loaded hypercharge), acting trivially on the four-channel span; the multiplicity-one premise is exhibited on the model group S4 (Appendix K §3.3, p.234), not on this action", "hypotheses": [ "None beyond total hypercharge 0 on the four displayed tensors: the retention statement needs no multiplicity-one and no channel-transitivity premise.", "Split G2(2) setting as registered; the §2.2 transitivity argument is NOT used (A1717-F02)." ], "physical_target": null, "quantifier": "Every coefficient vector on that span; the (1,1,1,1) ray is named as the instance the suite carries", "real_form": "Split G2(2) setting" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 230 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix K", "section": "§3.3, Reynolds-forced equal weights", "pdf_page": 241, "quote": "(Rev32.9, A1652 F01b/S330.7: through Rev32.8 this paragraph derived the ray from “a group average over a symmetry that acts transitively on the channels”, which is unavailable for both projectors.)" }, "caution": "This UV coefficient ray does not predict equal low-energy masses or select a symmetry-breaking compensator. Retention is not protection: excluding an unequal quartet is a separate claim, and it holds only under the trivial multiplicity-one premise, which Appendix K p.234 states as a premise exhibited on the model group S4 and does not derive for the registered four-channel action.", "candidate_ids": [ "C2-046" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-111" } ], "url": "/library-v2/LIB2-113/", "content_sha256": "36236cbc0673f708d32f73e1b72963cd3acbd1dcb1c25c686772f144c071335e", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-114", "entry_version": 7, "class": "CLAIM", "title": "The registered compensator candidates do not produce the hierarchy", "statement": "The banked enhanced-symmetry and compensator candidates fail to produce the target within-generation hierarchy while respecting the projected Yukawa channel census.", "scope": { "carrier": "The banked enhanced-symmetry and compensator candidates", "domain": "The registered candidate sweep, not all conceivable compensators.", "group": null, "hypotheses": [ "Use the stated F4, E6, B−L and Jvac candidates and the tested dual-VEV, perturbative-residue and spurion variants.", "Retain the A1048 allowed/forbidden channel census." ], "physical_target": null, "quantifier": "The explicitly tested candidates.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 230 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix K", "section": "§3.4, Candidate-compensator sweep", "pdf_page": 241, "quote": "A sweep of the banked enhanced-symmetry candidates was performed; each fails to produce the required complete within-generation hierarchy while respecting the projected channel census" }, "caution": "The finite sweep does not exclude unbanked non-perturbative, composite or other symmetry-breaking mechanisms.", "candidate_ids": [ "C2-045" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-112" }, { "type": "related_to", "target": "LIB2-113" } ], "url": "/library-v2/LIB2-114/", "content_sha256": "ba7ab62a3eef17d8565e622bb87fa52b9cfb710aaca8ce9747817e2f3abf66bd", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-115", "entry_version": 8, "class": "CLAIM", "title": "The unrestricted residue map can reproduce any positive Yukawa quartet", "statement": "The registered residue-incidence map has rank 4 over eight independent Z-factors, so free field residues can realize any positive Yukawa quartet.", "scope": { "carrier": "The log-residue incidence map on the four registered Yukawa channels", "domain": "Freedom of the unconstrained residue map, not residues derived from a parent.", "group": null, "hypotheses": [ "Use the stated four channel supports and eight independent positive residue factors.", "The common vertex normalization is fixed." ], "physical_target": null, "quantifier": "The registered construction and its stated hypotheses.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 230 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "analytic", "availability": "shipped" } ], "primary_source": { "component": "Appendix K", "section": "§3.5, Incidence rank", "pdf_page": 242, "quote": "The corresponding 4 × 8 incidence matrix has rank 4 (each channel carries a unique pivot Z-factor)." }, "caution": "Reproducing a quartet through free residues does not explain it; the parent must determine the residues and thresholds.", "candidate_ids": [ "C2-050" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-115/", "content_sha256": "376fbeab5bc533b5c24ea833c48378191a23df66ddf70f16e979d4fc12c9a0af", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-116", "entry_version": 7, "class": "CLAIM", "title": "The displayed one-loop trajectory produces only an order-one spread", "statement": "The displayed one-loop SM-plus-Dirac-neutrino trajectory from the democratic unit ray reaches (yu,yd,ye,yν) = (1.0207,0.9958,0.3959,0.3581) at MZ.", "scope": { "carrier": "The displayed perturbative Yukawa trajectory", "domain": "The displayed trajectory at MZ, not an all-threshold running theorem.", "group": null, "hypotheses": [ "Start from the democratic unit ray and use the source's one-loop SM-plus-Dirac-neutrino running." ], "physical_target": "Illustrative running Yukawa quartet", "quantifier": "The registered construction and its stated hypotheses.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 230 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix K", "section": "§3.5, Running setup", "pdf_page": 242, "quote": "One-loop SM-plus-Dirac-ν running from the democratic unit ray lands at MZ on" }, "caution": "This single perturbative trajectory does not exclude every threshold or non-perturbative mechanism.", "candidate_ids": [ "C2-051" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-113" } ], "url": "/library-v2/LIB2-116/", "content_sha256": "cc934bc73ea9fab5e790038de65ae3d33dfb44198c2e34f00f13a5b035864620", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-117", "entry_version": 8, "class": "CLAIM", "title": "The edge-uniform parent metric has zero relative Yukawa rank", "statement": "At the registered golden vacuum, the parent edge-residue map has rank 1 and relative rank 0 because all four Yukawa channels see the same product of edge-uniform positive metrics.", "scope": { "carrier": "The reflected cubic-cone kinetic metric and its three off-diagonal Peirce edges", "domain": "The edge-uniform two-derivative parent geometry, not arbitrary physical residues.", "group": null, "hypotheses": [ "Use GAB = ∂A∂B[−log N] at the registered unit-norm golden vacuum.", "Every loaded Yukawa vertex draws one field from each of the three Peirce edges." ], "physical_target": null, "quantifier": "The registered construction and its stated hypotheses.", "real_form": "J3(Os) with the registered reflected positive metric" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 231 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "analytic", "availability": "shipped" }, { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix K", "section": "§3.6, Edge-uniform metrics", "pdf_page": 242, "quote": "On the three off-diagonal Peirce edges the reflected positive metrics are component-uniform scalars," }, "caution": "The zero relative rank belongs to this parent geometry and does not exclude more general symmetry-breaking residues.", "candidate_ids": [ "C2-049" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-115" } ], "url": "/library-v2/LIB2-117/", "content_sha256": "74b1198234892e5f2219243fa0725534aea640c4d1129f33b453e193ac0fb8be", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-118", "entry_version": 7, "class": "CLAIM", "title": "The banked parent does not determine the within-generation hierarchy", "statement": "Within the banked exceptional-Jordan/loaded-gauge parent and its tested running and enhanced-symmetry set, the four distinct physical Yukawa coefficients are not determined.", "scope": { "carrier": "The banked invariant cubic, loaded-gauge parent and registered extensions", "domain": "The source's scoped negative, not a universal prohibition on coefficient derivations.", "group": null, "hypotheses": [ "Use the banked invariant structure, displayed perturbative one-loop running and enhanced-symmetry candidates." ], "physical_target": null, "quantifier": "The banked action and tested extensions only.", "real_form": "Loaded exceptional-Jordan framework" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 232 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix K", "section": "§1, Negative conclusion", "pdf_page": 238, "quote": "The four distinct physical coefficients {yu , yd , ye , yν } — i.e. the entire within-generation mass hierarchy — do not follow from the banked parent action." }, "caution": "The conclusion does not exclude an unbanked parent, non-perturbative dynamics or composite strong-coupling mechanisms.", "candidate_ids": [ "C2-048" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-113" }, { "type": "related_to", "target": "LIB2-114" }, { "type": "related_to", "target": "LIB2-115" }, { "type": "related_to", "target": "LIB2-116" }, { "type": "related_to", "target": "LIB2-117" } ], "url": "/library-v2/LIB2-118/", "content_sha256": "d149a491c547c1196726d496674e7f7af97395753599c33f6039f01cfcc7025d", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-119", "entry_version": 7, "class": "CLAIM", "title": "The same-block Peirce contraction extracts the unit middle weight", "statement": "In the registered same-block (1,3) Peirce carrier, the cubic invariant extracts the middle vacuum weight λ2 = 1.", "scope": { "carrier": "The same-block carrier fields and the golden vacuum contraction", "domain": "The internal carrier eigenvalue, not the literal cross-block Standard-Model Yukawa.", "group": null, "hypotheses": [ "Place the two carrier fields in the same (1,3) Peirce block.", "Use the source's Freudenthal cross-product and trace normalization." ], "physical_target": null, "quantifier": "The registered construction and its stated hypotheses.", "real_form": "J3(Os)" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 140 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "analytic", "availability": "shipped" } ], "primary_source": { "component": "Appendix A", "section": "§A.6, W01: internal carrier result", "pdf_page": 145, "quote": "the cubic invariant, evaluated on the carrier field ΦH in the (1, 3) Peirce block, extracts the middle vacuum weight λ2 = 1." }, "caution": "The unit carrier eigenvalue does not identify the physical Higgs, the renormalized coupling or the Planck scale.", "candidate_ids": [ "C2-016" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-108" } ], "url": "/library-v2/LIB2-119/", "content_sha256": "b3f7c3fba3390dd13c5b59bb868277a939118f9188c57a9f95e2d598a7150290", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-120", "entry_version": 8, "class": "CLAIM", "title": "W01 declares the Planck-scale top-Yukawa attachment", "statement": "Reading the carrier eigenvalue as yt(MPl) = 1 is the declared W01 attachment, requiring a physical Higgs direction, a scheme-specific coupling and an identification of the algebraic scale with MPl.", "scope": { "carrier": "The export of the unit carrier eigenvalue to a physical ultraviolet coupling", "domain": "The W01 ultraviolet boundary attachment and its three unproved identifications.", "group": null, "hypotheses": [ "Identify the carrier with the physical Higgs direction.", "Identify the vacuum weight with a renormalization-scheme-specific coupling.", "Identify the algebraic scale with MPl." ], "physical_target": "yt(MPl)", "quantifier": "The registered construction and its stated hypotheses.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 140 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix A", "section": "§A.6, W01: declared attachment", "pdf_page": 145, "quote": "Reading that eigenvalue as the physical top Yukawa at the Planck scale, yt (MPl ) = 1, is a declared attachment, not a derivation:" }, "caution": "This ultraviolet registration is not a proof of the physical coupling or its value after low-energy running and matching.", "candidate_ids": [ "C2-016" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "depends_on", "target": "LIB2-119" } ], "url": "/library-v2/LIB2-120/", "content_sha256": "3a3d76024012e41008ad44c4d7635fbd4e7fa9d3bf2982069b6cfc731704f29c", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-121", "entry_version": 11, "class": "CLAIM", "title": "The top tree estimate retains a status-ineligible cross-scheme offset", "statement": "The retained electroweak tree estimate mt = vEW/√2 is printed as 174,104 MeV; its +0.87% offset is cross-scheme and sets no status.", "scope": { "carrier": "The electroweak tree estimate using the measured Higgs VEV", "domain": "The displayed tree estimate and naive cross-scheme comparison, not a scheme-matched pole-mass prediction.", "group": null, "hypotheses": [ "Insert the measured vEW in the stated tree relation.", "Keep the W01 attachment and the distinction between ultraviolet and electroweak couplings." ], "physical_target": "mt tree estimate", "quantifier": "The registered construction and its stated hypotheses.", "real_form": null }, "source_labels_as_printed": { "math_status": "Structural", "attachment": "NOT_PRINTED", "scorecard_tier_word": "Structural", "pdf_page": 333 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix X", "section": "Table 4, Top row", "pdf_page": 354, "quote": "t anchor vEW / 2 (yt =1) 174,104 172,600 Structural (+0.87%; (re-tiered Rev29 ) dcmp =+5.57, [A632] cross- scheme, no status)" }, "caution": "The cross-scheme offset is not a physics tension; a scheme-matched conclusion requires the missing matching prescription.", "candidate_ids": [ "C2-017" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "depends_on", "target": "LIB2-120" }, { "type": "compares_with", "target": "SL-17" }, { "type": "rests_on_premise", "target": "PRM-028" } ], "url": "/library-v2/LIB2-121/", "content_sha256": "e310ac61a60f145dc2518cc5b623429743eef8b331b5344867f3237cd9cf2a95", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-122", "entry_version": 8, "class": "CLAIM", "title": "The muon-to-tau formula is a loaded reproduced ratio", "statement": "The retained ratio mµ/mτ = (ϕ/√5)^(8/3)·√2/10 = 0.059684 is Structural mathematically, Loaded-correspondence physically and Reproduced numerically.", "scope": { "carrier": "The compact muon-to-tau ratio formula", "domain": "The loaded dimensionless ratio, distinct from the tau-anchored mass and QED-matched mass.", "group": null, "hypotheses": [ "Use the dimension ratio as the mass exponent and the offered J2-based normalization.", "The coefficient provenance is target-first and the divide-by-dimension step is argued by analogy." ], "physical_target": "mµ/mτ", "quantifier": "The registered construction and its stated hypotheses.", "real_form": null }, "source_labels_as_printed": { "math_status": "Structural", "attachment": "Loaded-correspondence", "scorecard_tier_word": null, "pdf_page": 33 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 2", "section": "§3.2, Ratio typing", "pdf_page": 34, "quote": "The rows of this subsection therefore stand at Structural (mathematical tier), Loaded-correspondence (physical attachment) and Reproduced (numerical status): the ratio is reproduced, not derived." }, "caution": "Exact dimension quantities do not by themselves derive their use as a mass exponent and physical normalization.", "candidate_ids": [ "C2-056" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-049" }, { "type": "rests_on_premise", "target": "PRM-012" } ], "url": "/library-v2/LIB2-122/", "content_sha256": "9d208fe5a90a6b2582b6d3cd854a8d1ae35ee91cecb6a6d188bb999bc197e0af", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-123", "entry_version": 9, "class": "CLAIM", "title": "The muon-ratio residual is the multiplicative coefficient gap", "statement": "The +0.37% muon-to-tau residual is the multiplicative gap between Creq = 0.140894 and the offered C = 0.141421, not an additional correction above a completed derivation.", "scope": { "carrier": "The required and offered coefficients of the muon-to-tau formula", "domain": "Interpretation of the existing coefficient gap, not a proposed correction.", "group": null, "hypotheses": [ "The coefficient multiplies the entire registered ratio formula.", "Use the source's required and offered values, without a new fit." ], "physical_target": "Provenance of the muon-to-tau ratio residual", "quantifier": "The registered construction and its stated hypotheses.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 33 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 2", "section": "§3.2, Required coefficient", "pdf_page": 35, "quote": "is Creq = 0.140894;" }, "caution": "The separate QED matching step does not supply the missing derivation of this coefficient or erase its target-first provenance.", "candidate_ids": [ "C2-056" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-122" } ], "url": "/library-v2/LIB2-123/", "content_sha256": "5e04be3564295b83a9c34b711191fc1a5e703dc122ceab7a3c7ae3c49dbf0676", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-124", "entry_version": 8, "class": "CLAIM", "title": "The mass-formula chains retain three named dimensional anchors", "statement": "The current formula chains use mτ = 1776.93 MeV, vEW = 246.22 GeV and ΛG2 ≈ 260 MeV as three named dimensional anchors, a usage inventory distinct from the abstract scale-class count.", "scope": { "carrier": "The operational dimensional anchors in the mass-formula chains", "domain": "The formula-usage inventory, not a derivation of the dimensional inputs.", "group": null, "hypotheses": [ "Retain the input-count convention separating an abstract scale class, external calibrations and named operational anchors." ], "physical_target": null, "quantifier": "The registered construction and its stated hypotheses.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 334 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix X", "section": "Table 4, Named operational anchors", "pdf_page": 355, "quote": "mτ = 1776.93 MeV (lepton tower + mb via 7/3); vEW = 246.22 GeV (top, pinned by GF ); ΛG2 ≈ 260 MeV (light-quark constituents + mc via 7/3)." }, "caution": "The abstract one-class theorem does not by itself supply the relations and uncertainties connecting these empirical anchors.", "candidate_ids": [ "C2-113" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-056" } ], "url": "/library-v2/LIB2-124/", "content_sha256": "31681083fdb403f09a4e230b1df1b4b59d7e54516f5122eb7ddc29676e582049", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-125", "entry_version": 8, "class": "CLAIM", "title": "The tau-anchored muon tree estimate inherits the loaded ratio", "statement": "Applying the retained muon-to-tau ratio to the measured tau anchor gives the tree estimate mµ = 106.05 MeV, with the printed +0.37% offset.", "scope": { "carrier": "The dimensionful muon tree estimate", "domain": "The tree value before the separate QED matching step.", "group": null, "hypotheses": [ "Use the loaded ratio of Paper 2, Eq. (17), and the measured tau anchor." ], "physical_target": "Muon tree mass", "quantifier": "The registered construction and its stated hypotheses.", "real_form": null }, "source_labels_as_printed": { "math_status": "Structural", "attachment": "Loaded-correspondence", "scorecard_tier_word": null, "pdf_page": 34 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 2", "section": "§3.2, Tau anchor", "pdf_page": 34, "quote": "mτ = 1776.93(9) MeV," }, "caution": "This mass estimate inherits the target-first coefficient gap and is not independent of the measured tau anchor.", "candidate_ids": [ "C2-018" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "depends_on", "target": "LIB2-122" }, { "type": "uses_input", "target": "LIB2-124" }, { "type": "related_to", "target": "LIB2-123" }, { "type": "rests_on_premise", "target": "PRM-019" } ], "url": "/library-v2/LIB2-125/", "content_sha256": "6f4a19cd53204689f1f07a3cf05c511c0c4b104d6cf856fa106b9d6e85ca7091", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-126", "entry_version": 9, "class": "CLAIM", "title": "The separate QED matching step gives the displayed physical muon mass", "statement": "The stated QED matching step divides the muon tree value by 1 + δQED, with δQED = +0.3125%, giving mµ,phys = 105.7233 MeV.", "scope": { "carrier": "The QED-matched muon mass", "domain": "The stated matching step, not a derivation of the tree normalization.", "group": null, "hypotheses": [ "Start from the retained loaded tree estimate.", "Use the supplied one-loop QED matching prescription, α and the hadronic matching scale." ], "physical_target": "QED-matched muon mass", "quantifier": "The registered construction and its stated hypotheses.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 34 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 2", "section": "§3.2, Step (3): physical mass", "pdf_page": 35, "quote": "Physical muon mass: mµ,phys = mtreeµ /(1 + δQED ) = 105.7233 MeV (+0.061% PDG; Appendix X carries the rounded +0.06%)." }, "caution": "The QED correction does not derive the loaded coefficient or account for its separate fit gap.", "candidate_ids": [ "C2-019" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "depends_on", "target": "LIB2-125" }, { "type": "related_to", "target": "LIB2-123" }, { "type": "rests_on_premise", "target": "PRM-008" } ], "url": "/library-v2/LIB2-126/", "content_sha256": "d56323618efbf640d092b6b6576adb8ad8e8c56d8a10c9c4edf0d1f97df5b8ef", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-127", "entry_version": 7, "class": "CLAIM", "title": "The electron value is the light Koide root under an external empirical rule", "statement": "With the measured tau anchor and QED-matched muon mass, the external empirical Koide rule K = 2/3 gives the selected light root me = 0.5076 MeV.", "scope": { "carrier": "The charged-lepton Koide closure with its selected light branch", "domain": "The Koide-consistent electron chain, not an algebra-only mass derivation.", "group": null, "hypotheses": [ "Use the external empirical relation K = 2/3.", "Supply the measured tau mass and the preceding QED-matched muon chain.", "Select the light positive root as in the source." ], "physical_target": "Koide-consistent electron mass", "quantifier": "The registered construction and its stated hypotheses.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 34 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 2", "section": "§3.2, External Koide premise", "pdf_page": 36, "quote": "The electron mass is determined by the external empirical relation K = 2/3 acting on that mµ chain and the measured mτ anchor [A636, A637]." }, "caution": "This empirical-rule closure does not derive the electron mass from the bare Jordan algebra or remove the muon-chain loading.", "candidate_ids": [ "C2-020", "C2-057" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "depends_on", "target": "LIB2-126" }, { "type": "uses_input", "target": "LIB2-124" }, { "type": "rests_on_premise", "target": "PRM-019" }, { "type": "rests_on_premise", "target": "PRM-030" } ], "url": "/library-v2/LIB2-127/", "content_sha256": "43276a80bd768e5ab0aab62b0890aca960cb7b0d8313f81ea25fd509b9a41d96", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-128", "entry_version": 7, "class": "CLAIM", "title": "The light-quark constituent proxy uses the fitted hadronic anchor", "statement": "The retained light-quark constituent relation is m_u^const ≈ m_d^const ≈ ΛG2 ϕ^(1/2) ≈ 331 MeV.", "scope": { "carrier": "The up/down constituent-mass proxy", "domain": "Constituent masses, not current-quark masses in a renormalization scheme.", "group": null, "hypotheses": [ "Use the fitted hadronic anchor ΛG2 and the stated leading-order constituent relation." ], "physical_target": "Light-quark constituent masses", "quantifier": "The registered construction and its stated hypotheses.", "real_form": null }, "source_labels_as_printed": { "math_status": "Structural", "attachment": "NOT_PRINTED", "scorecard_tier_word": "Structural", "pdf_page": 334 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 2", "section": "§3.4, Equation (19): constituent relation", "pdf_page": 36, "quote": "mconst u ≈ mconst d ≈ ΛG2 φ1/2 ≈ 331 MeV," }, "caution": "This constituent proxy is not directly comparable to current-quark masses and does not derive the hadronic anchor.", "candidate_ids": [ "C2-023" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "uses_input", "target": "LIB2-124" }, { "type": "rests_on_premise", "target": "PRM-029" } ], "url": "/library-v2/LIB2-128/", "content_sha256": "0a85437081438593bbac3e72e180f41a9e513a5971764e978e5a9bf4fed2b84b", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-129", "entry_version": 7, "class": "CLAIM", "title": "The strange constituent proxy carries the printed Casimir modifier", "statement": "The source gives m_s^const = ΛG2 ϕ(KG2/KSU(3))^(1/4) = 553.7 MeV for the strange constituent proxy.", "scope": { "carrier": "The strange constituent-mass proxy", "domain": "The constituent input to the charm bridge, not an MS-bar strange mass.", "group": null, "hypotheses": [ "Use the fitted hadronic anchor and the source’s G2-to-SU(3) Casimir modifier.", "Use the stated geometric-mean prescription for the long- and short-root scales." ], "physical_target": "Strange constituent proxy", "quantifier": "The registered construction and its stated hypotheses.", "real_form": null }, "source_labels_as_printed": { "math_status": "Structural", "attachment": "NOT_PRINTED", "scorecard_tier_word": "Structural", "pdf_page": 334 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 2", "section": "§3.4, Casimir and geometric-mean prescription", "pdf_page": 36, "quote": "the G2 Langlands-self-dual geometric mean of the long-/short-root scales (the geometric mean m2s = mshort mlong is exact under G2 root-system self-duality, s194)" }, "caution": "This constituent proxy does not supply a constituent-to-MS conversion or derive the hadronic scale.", "candidate_ids": [ "C2-022" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "uses_input", "target": "LIB2-124" }, { "type": "rests_on_premise", "target": "PRM-029" } ], "url": "/library-v2/LIB2-129/", "content_sha256": "339959a0572b5cbafad92f6e9a66835f40210eb529f3cde424e40f1bdf90e64f", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-130", "entry_version": 9, "class": "CLAIM", "title": "The bottom bridge retains its tau anchor and cross-scheme offset", "statement": "The retained bottom bridge mb = (7/3)mτ = 4146 MeV has the printed −0.95% offset from the MS-bar comparator, a cross-scheme comparison that sets no status.", "scope": { "carrier": "The tau-anchored bottom boundary value", "domain": "The boundary-value correspondence without a completed low-energy scheme-matching theorem.", "group": null, "hypotheses": [ "Apply the retained 7/3 bridge to the measured tau mass.", "Keep the framework boundary value distinct from the MS-bar comparator mb(mb)." ], "physical_target": "Bottom boundary-value mass", "quantifier": "The registered construction and its stated hypotheses.", "real_form": null }, "source_labels_as_printed": { "math_status": "Structural", "attachment": "NOT_PRINTED", "scorecard_tier_word": "Structural", "pdf_page": 334 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 2", "section": "§3.6, Bottom comparison and status rule", "pdf_page": 38, "quote": "The mb row must be quoted with its offset: mb = (7/3)mτ = 4146 MeV against PDG 2026 mb (mb ) = 4186 ± 6 MeV is −0.95% and dcmp = −6.64 (cross-scheme, no status; full precision, Rev32.9)." }, "caution": "The bridge is not a derived low-energy MS-bar mass relation, and its comparator distance is not a scheme-matched tension.", "candidate_ids": [ "C2-021" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "uses_input", "target": "LIB2-124" }, { "type": "related_to", "target": "LIB2-053" }, { "type": "compares_with", "target": "SL-16" }, { "type": "rests_on_premise", "target": "PRM-019" } ], "url": "/library-v2/LIB2-130/", "content_sha256": "338021a22147d0d3ea4e1b64c7f597a0eed7e5d8052c50938e137828f999f35d", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-131", "entry_version": 10, "class": "CLAIM", "title": "The charm bridge remains constituent-anchored and cross-scheme", "statement": "The retained charm bridge mc = (7/3)m_s^const = 1291.9 MeV has the printed +1.49% offset from its MS-bar comparator; no constituent-to-MS conversion uncertainty is supplied.", "scope": { "carrier": "The constituent-anchored charm boundary value", "domain": "The cross-scheme boundary-value comparison, not a matched significance.", "group": null, "hypotheses": [ "Use the displayed strange constituent proxy in the retained 7/3 bridge.", "The comparator is mc(mc) in MS-bar; no conversion prescription with uncertainty is supplied." ], "physical_target": "Charm boundary-value mass", "quantifier": "The registered construction and its stated hypotheses.", "real_form": null }, "source_labels_as_printed": { "math_status": "Structural", "attachment": "NOT_PRINTED", "scorecard_tier_word": "Structural", "pdf_page": 333 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 2", "section": "§3.6, Charm offset and comparator", "pdf_page": 38, "quote": "The charm bridge value mc = 1291.9 MeV lies +1.49% above the PDG 2026 MS comparator mc (mc ) = 1272.9 ± 4.5 MeV." }, "caution": "This constituent-anchored comparison does not establish a low-energy mass theorem or a status-setting discrepancy.", "candidate_ids": [ "C2-022" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "depends_on", "target": "LIB2-129" }, { "type": "related_to", "target": "LIB2-053" }, { "type": "compares_with", "target": "SL-15" } ], "url": "/library-v2/LIB2-131/", "content_sha256": "1c449b540638df9dc0e53525c0309cea8b8ef439ea3c0e03c913646a38a8e283", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-132", "entry_version": 7, "class": "CLAIM", "title": "The tested untuned running and matching readings do not remove the heavy-quark offsets", "statement": "The tested untuned SM/QCD running-and-matching readings do not remove the top, bottom and charm boundary-value offsets.", "scope": { "carrier": "The tested heavy-quark boundary values and matching-scale readings", "domain": "The specific running/matching audit, not a universal exclusion of threshold effects.", "group": null, "hypotheses": [ "Use the source’s top pole/MS alternatives, bottom self-scale and tau-scale alternatives, and strange-constituent-scale charm running.", "No matching scale is tuned to the target." ], "physical_target": null, "quantifier": "The registered construction and its stated hypotheses.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 38 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 2", "section": "§3.6, Heavy-quark RG/matching audit", "pdf_page": 39, "quote": "were tested against standard SM/QCD running and matching with no" }, "caution": "The negative audit does not exclude all threshold physics or turn the cross-scheme offsets into matched statistical tensions.", "candidate_ids": [ "C2-017", "C2-021", "C2-022" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-121" }, { "type": "related_to", "target": "LIB2-130" }, { "type": "related_to", "target": "LIB2-131" } ], "url": "/library-v2/LIB2-132/", "content_sha256": "afadd96648e31067674924b9b144b1c8b4702b39a67e4fc44d7293de44af4452", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-133", "entry_version": 7, "class": "CLAIM", "title": "The outer-mirror charged-lepton fit consumes two free gaps", "statement": "With the loaded amplitude modes held fixed, the outer-mirror operator reproduces the charged-lepton ratios using the two fitted gaps µp = 1.5314 and µd = 0.9313.", "scope": { "carrier": "The outer-mirror operator Hout = µd Pd + µp P⊥", "domain": "The operator-route fit, separate from the compact algebraic ratio formula.", "group": null, "hypotheses": [ "Hold the singular values of the loaded circulant A fixed.", "Fit the two free gaps to the two charged-lepton ratios." ], "physical_target": "Fitted charged-lepton ratio reproduction", "quantifier": "The registered construction and its stated hypotheses.", "real_form": null }, "source_labels_as_printed": { "math_status": "Input", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 261 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix O", "section": "§5, Outer-mirror operator", "pdf_page": 275, "quote": "Hout = µd Pd + µp P⊥ ," }, "caution": "Fitting two gaps to two ratios provides no prediction of those fitted ratios and does not reconcile the two mass routes.", "candidate_ids": [ "C2-056" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-122" } ], "url": "/library-v2/LIB2-133/", "content_sha256": "49ce635659ff7bd5411a0c90dda9dce0d4379c662e0f01b8b414bae700a2455a", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-134", "entry_version": 8, "class": "CLAIM", "title": "The literal Jordan-adjoint neutrino mass reading fails its splitting-ratio test", "statement": "The literal d = 1 Jordan-adjoint mass reading gives the neutrino splitting ratio 0.27639 against the measured 0.03002, too large by the printed factor 9.21.", "scope": { "carrier": "The literal eigenvalue-to-mass reading of the Jordan-adjoint mixing carrier", "domain": "The d = 1 physical mass interpretation, not the internal mixing geometry or the distinct selected edge target.", "group": null, "hypotheses": [ "Set the physical masses proportional to the eigenvalues as in the literal reading.", "Use the NuFIT 6.1 IC24 normal-ordering splitting-ratio comparator stated on the page." ], "physical_target": "Literal neutrino splitting-ratio reading", "quantifier": "The registered construction and its stated hypotheses.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 80 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 5", "section": "§2, Literal mass reading", "pdf_page": 84, "quote": "the literal reading mi ∝ λi (Xν ) predicts normal ordering but gives the scale-free ratio" }, "caution": "This failed mass interpretation does not refute the internal mixing carrier or derive an absolute neutrino mass scale.", "candidate_ids": [ "C2-024", "C2-126" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "compares_with", "target": "SL-01" }, { "type": "compares_with", "target": "SL-02" } ], "url": "/library-v2/LIB2-134/", "content_sha256": "14da3b710a65b66358b2c35c837990f5856d6b022e508f40f480fcde5b9ef18a", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-135", "entry_version": 8, "class": "CLAIM", "title": "The spectral-gap model imposes its self-consistency through the lifted cone trace", "statement": "In the stated spectral-singularity model, T(ε) = A/ε and ε = m² = αA give αT = 1 and the scale relation Λ² = αA.", "scope": { "carrier": "The lifted null-cone eigenspace and its spectral trace", "domain": "The structural spectral-singularity mechanism, not a numerical prediction of the confinement scale.", "group": null, "hypotheses": [ "Lift the stated eigenspace by the mass parameter ε.", "Let A be the cone-Hessian trace over the lifted sector and impose the printed self-consistency condition." ], "physical_target": null, "quantifier": "The registered construction and its stated hypotheses.", "real_form": "The registered cubic-norm cone" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 209 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix I", "section": "§6, Proposition 6.3: trace and self-consistency", "pdf_page": 218, "quote": "Lifting the null-cone eigenspace by a mass ε gives a spectral trace T (ε) = A/ε, with A the trace of the cone Hessian over the lifted sector." }, "caution": "The relation does not determine a numerical confinement scale independently of its coupling and calibration inputs.", "candidate_ids": [ "C2-160" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-128" } ], "url": "/library-v2/LIB2-135/", "content_sha256": "34ea7dfca662c55c866d89d4dbcbb06dc465d073d01e0059bf4ba228232f6423", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-136", "entry_version": 7, "class": "CLAIM", "title": "The baryonic cubic channel is distinct from the cancelled quadratic channel", "statement": "In the registered cubic-norm argument, the baryonic channel uses the cubic polarization of N rather than the bilinear evaluation form, so the stated quadratic cancellation does not act on it.", "scope": { "carrier": "The baryonic cubic polarization compared with the mesonic bilinear channel", "domain": "The source’s tensor-structure distinction, not a numerical baryon/meson mass ratio.", "group": null, "hypotheses": [ "Use the cubic polarization and quadratic trace form specified in Proposition 6.2." ], "physical_target": null, "quantifier": "The registered construction and its stated hypotheses.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 209 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix I", "section": "§6, Proposition 6.2: baryonic tensor", "pdf_page": 218, "quote": "The baryonic channel is built instead on the cubic polarization of N — the εabc εijk contraction (colour × generation), i.e. the Λ3 → singlet / determinant trilinear." }, "caution": "The tensor distinction is not a derived baryon spectrum, a mass ratio or an independently constructed physical residue.", "candidate_ids": [ "C2-156" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-058" }, { "type": "related_to", "target": "LIB2-135" } ], "url": "/library-v2/LIB2-136/", "content_sha256": "5c5f32f9033c29b5ab3be33e4385b7b3f65181f70d2335f1bd459567cebb8676", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-137", "entry_version": 8, "class": "CLAIM", "title": "The cone expansion uses a spectral background rather than stationarity of the cubic", "statement": "The source organizes the cone expansion at Jvac by the Hessian spectrum rather than stationary phase of N, because ∇N ≠ 0 there.", "scope": { "carrier": "The cone-Hessian expansion about the registered spectral background", "domain": "The spectral-background interpretation of this expansion, not the full gauged-potential stability question.", "group": null, "hypotheses": [ "Use the cubic norm N and the Hessian G in Appendix I, Remark 6.4." ], "physical_target": null, "quantifier": "The registered construction and its stated hypotheses.", "real_form": "The registered cubic-norm cone" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 209 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix I", "section": "§6, Remark 6.4(i): spectral background", "pdf_page": 219, "quote": "The vacuum is a spectral background, not a saddle: Jvac is selected by the eigenvalue structure of G, not by ∇N = 0 (indeed ∇N = ̸ 0 there)," }, "caution": "This expansion prescription does not establish a stationary or stable vacuum of a different gauged or sourced action.", "candidate_ids": [ "C2-171" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-135" } ], "url": "/library-v2/LIB2-137/", "content_sha256": "931e354fda7fde3f4cb37fc5af47db13fc0f09e6815e6dab401f6e3702d5d32f", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-138", "entry_version": 8, "class": "CLAIM", "title": "The compact two-scale Gram class excludes its previously priced half-ratio", "statement": "Intersecting the compact two-scale ansatz with the plane-preserving, coset-compatible, SM-invariant Gram family gives l = c and r = l/c = 1, excluding r = 1/2 in that declared class.", "scope": { "carrier": "The compact quark/lepton two-scale Gram ansatz", "domain": "The declared D1176–D1180 Gram class, not the earlier dimensional-calibration inventory.", "group": null, "hypotheses": [ "Use gQ = gu = gd = c and gL = gν = ge = l.", "Restrict to the plane-preserving, coset-compatible, SM-invariant Gram family." ], "physical_target": null, "quantifier": "The registered construction and its stated hypotheses.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 351 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix X", "section": "§4.3, Collapse to the scalar line", "pdf_page": 373, "quote": "with the plane-preserving, coset-compatible, SM-invariant Gram family leaves only the scalar line l = c. Hence r = l/c = 1 exactly, and the previously priced point r = 1/2 is excluded in this declared natural class." }, "caution": "The exclusion is not universal and does not refute the distinct finite 7/3 index or unification-ratio statement.", "candidate_ids": [ "C2-110" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-117" }, { "type": "related_to", "target": "LIB2-053" } ], "url": "/library-v2/LIB2-138/", "content_sha256": "b4d6d61e9b9832646b46134422ceebc85efef50b0d0e77bf33fa2d7a70c00821", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-139", "entry_version": 7, "class": "CLAIM", "title": "The declared top-Yukawa boundary has a separately reported running value", "statement": "The suite reports that RG evolution of its declared yt(MPl) = 1 boundary gives yt(MZ) ≈ 0.967 in the low-energy effective theory.", "scope": { "carrier": "The top-Yukawa running trajectory from the declared ultraviolet boundary", "domain": "The reported running value, distinct from the electroweak tree mass estimate.", "group": null, "hypotheses": [ "Use the W01 ultraviolet attachment and the running prescription reported by the suite." ], "physical_target": "Top Yukawa at MZ", "quantifier": "The registered construction and its stated hypotheses.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 36 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 2", "section": "§3.5, Declared ultraviolet boundary", "pdf_page": 37, "quote": "its reading as the physical top Yukawa at the Planck scale is the declared attachment W01 (Appendix A, interface marker W01) — an attachment, not a derivation (Rev32.5, A1564)." }, "caution": "The running value inherits W01 and does not equate the two scale-dependent couplings or complete the top-mass matching.", "candidate_ids": [ "C2-016" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "depends_on", "target": "LIB2-120" }, { "type": "related_to", "target": "LIB2-121" }, { "type": "rests_on_premise", "target": "PRM-027" } ], "url": "/library-v2/LIB2-139/", "content_sha256": "0ef84e1ebb55c7bcc53cb5399ec5611887a62dd6e01cc0379002aac5908b9ab9", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-140", "entry_version": 9, "class": "CLAIM", "title": "The selected neutrino rung is a below-floor edge target, not a mass relation", "statement": "The selected rung R2 = 1/(ϕ⁴ − 1) = 0.17082, whose square is 0.02918, is typed as a Δm²21/Δm²31 ratio prediction with m1 = 0 asserted (R144): a JUNO-decidable falsifier that stands only under normal ordering and m1 ≲ 1 meV. Its earlier typing as a below-floor edge target is superseded.", "scope": { "carrier": "The selected d = 2 resolvent rung and the normal-ordering mass-ratio floor", "domain": "The selected edge reading, distinct from the falsified literal d = 1 reading.", "group": null, "hypotheses": [ "Use the selected d(ν) = 2 registration.", "The source's exact asymmetric comparison uses NuFIT 6.1 without and with SK-ATM." ], "physical_target": "Selected neutrino mass-ratio edge target", "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "Structural", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 80 }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Paper 5", "section": "§2, Two readings, one family: selected rung", "pdf_page": 84, "quote": "at d = 2, mν2 /mν3 = R2 = 1/(ϕ4 − 1) = 0.17082, so the ratio channel reads R22 = 0.02918 against" }, "caution": "The edge does not predict equality with a physical mass ratio or derive normal ordering, the rung assignment or the absolute neutrino mass scale.", "candidate_ids": [ "C2-127" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-134" }, { "type": "compares_with", "target": "SL-01" }, { "type": "compares_with", "target": "SL-02" }, { "type": "compares_with", "target": "SL-03" } ], "url": "/library-v2/LIB2-140/", "content_sha256": "4a8de050857299262bffedb215ad228909f37db77b066c6cbb755026ba1af5ed", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-141", "entry_version": 8, "class": "CLAIM", "title": "The neutrino depth assignment is post-hoc and receives no blind credit", "statement": "The assignment d(ν) = 2 is reproduced by the post-hoc rule d = 2 + [YR ≠ 0] + [coloured], with a printed local-band look-elsewhere range of 10.9–13.9% and no blind credit.", "scope": { "carrier": "The post-hoc feature rule and injective depth assignment", "domain": "The provenance of the selected depth, not an independent selector theorem.", "group": null, "hypotheses": [ "Use the feature indicators and assignment family stated in Paper 5." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 80 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" }, { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Paper 5", "section": "§2, Post-hoc depth rule", "pdf_page": 84, "quote": "The assignment d(ν) = 2 is selected, not derived: it is reproduced by the post-hoc feature rule d = 2 + [YR ̸= 0] + [coloured]" }, "caution": "This post-hoc rule is not a theory-selected assignment, and its fit preference does not supply a physical neutrino mass operator.", "candidate_ids": [ "C2-127" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-140" } ], "url": "/library-v2/LIB2-141/", "content_sha256": "fd900eec21dc929e2da765236f744edf5c97f7f214674da08a9fb2e6880afd48", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-142", "entry_version": 8, "class": "CLAIM", "title": "The lightest-mass boundary has mass-sum and beta-decay corollaries", "statement": "At the m1 = 0 normal-ordering boundary, the suite gives Σmν = 58.79 meV and mβ = 8.74 meV as boundary properties, not consequences of R2.", "scope": { "carrier": "The normal-ordering boundary with a vanishing lightest mass", "domain": "The stated boundary corollaries, distinct from selecting a rung or deriving a mass scale.", "group": null, "hypotheses": [ "Set m1 = 0 and assume normal ordering.", "Use the splitting and mixing inputs of the source's boundary calculation." ], "physical_target": "Normal-ordering boundary mass sum and beta-decay mass", "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 80 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 5", "section": "§2, Boundary corollaries", "pdf_page": 85, "quote": "If the edge is taken at the boundary m1 = 0 with normal ordering, the boundary itself fixes Σmν = 58.79 meV and mβ = 8.74 meV." }, "caution": "These boundary values do not derive the R2 attachment, an absolute neutrino mass scale from the algebra, or a cosmological exclusion.", "candidate_ids": [ "C2-127" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-140" } ], "url": "/library-v2/LIB2-142/", "content_sha256": "630ca0cb9a4b86587730df47047988c72847dc1f0dd3a823e73aefa56d14eca9", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-143", "entry_version": 8, "class": "CLAIM", "title": "The exhibited winding-to-Fibonacci functor defines the finite cluster image", "statement": "The exhibited functor has Fφ([N]) = τ⊗N, sends the mirror to the dagger and kills the four-strand Jones–Wenzl projector, Fφ(f4) = 0.", "scope": { "carrier": "The registered winding category and its Fibonacci-category image", "domain": "The finite functor and morphism-weight image, not a continuum or energy-producing map.", "group": null, "hypotheses": [ "Use the exhibited generator set at δ = φ and the quotient killing f4." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 126 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Paper 9", "section": "§2.1, The exhibited functor", "pdf_page": 130, "quote": "Fφ sends the winding category to the Fibonacci category: objects Fφ ([N ]) = τ ⊗N ; the mirror is the dagger; the four-strand Jones–Wenzl projector is killed, Fφ (f4 ) = 0" }, "caution": "The finite functor does not construct a continuum Yang–Mills functor or convert a categorical weight into an energy without the declared interface.", "candidate_ids": [ "C2-073" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-143/", "content_sha256": "f58b2a328bcca19582eaf170db0602f163aa52e11beb7b8c410cfe82d6c0f123", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-144", "entry_version": 12, "class": "CLAIM", "title": "The cluster-ledger interface is the declared weight-to-energy map", "statement": "The categorical construction fixes the ledger weights Tn; the declared cluster-ledger interface carries them to dimensionless nuclear binding energies B(nα)/√σ, together with the alpha-cell term nBα and the net triple-alpha associator weight T3.", "scope": { "carrier": "The n-fold alpha-composite ledger and its declared energy interface", "domain": "The constructed-weight to physical-energy attachment, not an energy carried by an associativity axiom.", "group": null, "hypotheses": [ "Use the cluster-ledger interface in Paper 9, Eq. (2).", "The string-tension unit is supplied separately when energies are expressed in MeV." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 126 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 9", "section": "§1, Weight and interface distinction", "pdf_page": 130, "quote": "fixes the ledger weights Tn , which the declared cluster-ledger interface (2) then carries to nuclear binding energies" }, "caution": "The interface does not derive the absolute energy unit or make the categorical associativity identity itself an energy.", "candidate_ids": [ "C2-073", "C2-077" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-143" }, { "type": "related_to", "target": "LIB2-148" } ], "url": "/library-v2/LIB2-144/", "content_sha256": "67a8e479f765e607533e3da16ba764a1f76523f0cc4461fb2682eb4c65a531d8", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-145", "entry_version": 9, "class": "CLAIM", "title": "The small-nucleus kernel is triangularly saturated", "statement": "For A ≤ 4, three new phi coefficients were tested on three new nuclei with a triangular dependency, leaving zero net overdetermination and no blind credit for the coefficient choice.", "scope": { "carrier": "The small-nucleus binding rule of Paper 9, Eq. (1)", "domain": "The A ≤ 4 calibration structure; later continuations carry the discriminating test.", "group": null, "hypotheses": [ "Use the initial coefficient set and triangular dependency described in the freedom audit." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 128 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 9", "section": "§3, Small-nucleus freedom audit", "pdf_page": 132, "quote": "Freedom audit (carried verbatim): the rule introduced three new φ-coefficients and was scored on three new nuclei with a triangular dependency — zero net overdetermination within A ≤ 4, so no blind credit for the coefficient choice." }, "caution": "The initial fit does not independently predict the nuclei used to fix its coefficients or establish the later continuations.", "candidate_ids": [ "C2-076" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-143" } ], "url": "/library-v2/LIB2-145/", "content_sha256": "9d596fc0706c97821760c5ec2c41365467b28f19e7a1d45a1a19851e0f4573d2", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-146", "entry_version": 10, "class": "CLAIM", "title": "The closed alpha-cell typing gives the A = 5 gap", "statement": "With f4 = 0 closing the alpha cell, a fifth nucleon is an external τ-line with no scalar channel, so the registered single-nucleon attachment to alpha is unbound.", "scope": { "carrier": "The closed alpha cell and an added nucleon", "domain": "The A = 5 gap within the registered cluster construction.", "group": null, "hypotheses": [ "Use the frozen closed-cell typing f4 = 0 and the external τ-line assignment." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 128 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 9", "section": "§4, Theorem 4.1: A = 5 gap", "pdf_page": 132, "quote": "f4 = 0 closes the α cell, so a fifth nucleon is an external τ -line with no scalar channel: no single nucleon binds to α." }, "caution": "The gap depends on the registered cell typing and does not determine the full charge-magnitude sector.", "candidate_ids": [ "C2-074" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-143" }, { "type": "related_to", "target": "LIB2-145" } ], "url": "/library-v2/LIB2-146/", "content_sha256": "ccf2d835373747b9f478939825d09a1804bb0ae56c205aca841062a029148ea9", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-147", "entry_version": 9, "class": "CLAIM", "title": "The two-alpha typing gives a negative first correction at A = 8", "statement": "In the registered two-alpha channel, no leading bridge is typeable; B(8Be) = 2Bα at leading order, and the first annular correction has Sαα = −ϕ⁻¹⁸√σ < 0.", "scope": { "carrier": "The two closed alpha cells and the virtual ττ̄ annulus", "domain": "The A = 8 gap and its first correction, not a complete two-circulation or shell model.", "group": null, "hypotheses": [ "Use α ⊗ α = 1 ⊗ 1 and the registered first annular correction." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 128 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 9", "section": "§4, Theorem 4.2: leading two-alpha relation", "pdf_page": 132, "quote": "α ⊗ α = 1 ⊗ 1 exposes no τ -line: no bridge is typeable, B(8 Be) = 2Bα √ at leading order" }, "caution": "This channel result does not give a complete nuclear Hamiltonian or settle the separate charge and breathing-accounting problems.", "candidate_ids": [ "C2-074" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-143" }, { "type": "related_to", "target": "LIB2-146" } ], "url": "/library-v2/LIB2-147/", "content_sha256": "906a1e5a74bfef0d39908d8ca4f6715b7bb3c635b020839173ad8fda811eb121", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-148", "entry_version": 7, "class": "CLAIM", "title": "The composition ladder is a finite trace invariant", "statement": "The finite composition weights obey Tn = (n − 2) + εn with εn = trϕ(Rn), where the trace is taken on the residual boundary-circulation class in the stated Temperley–Lieb quotient.", "scope": { "carrier": "The n-gon flip graph and residual boundary-circulation class", "domain": "The finite trace weight, before its declared binding-energy attachment.", "group": null, "hypotheses": [ "Use the quotient TLφ/⟨f4⟩ and its registered Markov trace." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 129 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 9", "section": "§6, Equation (3): trace ladder", "pdf_page": 133, "quote": "Tn = (n − 2) + εn , εn = trϕ (Rn )" }, "caution": "The finite trace law does not on its own derive a binding energy or a continuum Yang–Mills functor.", "candidate_ids": [ "C2-077" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-143" }, { "type": "related_to", "target": "LIB2-144" } ], "url": "/library-v2/LIB2-148/", "content_sha256": "193fbb8203b218b098f4475e0d192dc59f277ae3aef800a16d625ce616f0bc63", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-149", "entry_version": 8, "class": "CLAIM", "title": "The residual-circulation weights obey the printed piecewise rule", "statement": "The registered residual trace weights are ε5 = −ϕ⁻², ε6 = 0 and εn = ϕ^(5−n) for n ≥ 7.", "scope": { "carrier": "The residual boundary-circulation weights in the finite n-gon quotient", "domain": "The three cases of the finite trace-selection rule.", "group": null, "hypotheses": [ "Use the quotient and Markov trace of the composition ladder.", "The pentagon, hexagon and higher-cell cases have the source's specified annular typing." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 129 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 9", "section": "§6, Pentagon residual trace", "pdf_page": 133, "quote": "ε5 = −φ−2 (the pentagon F -move coherence loop: the killed channel appears once, negative trace)," }, "caution": "The piecewise weight rule does not by itself define a physical energy correction or justify an untyped change to a binding formula.", "candidate_ids": [ "C2-077" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-148" }, { "type": "related_to", "target": "LIB2-144" } ], "url": "/library-v2/LIB2-149/", "content_sha256": "fe0dccdd211bcf83c37e8d3c29da4d859a5f6566da031df2df98f94ce13e8fc3", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-150", "entry_version": 7, "class": "CLAIM", "title": "The suite reports a sealed pentagon-weight match", "statement": "The suite reports that the derived pentagon weight T5 = ϕ² = 2.618034 matched the sealed implied value 2.617965 at 26 ppm.", "scope": { "carrier": "The pentagon weight and the source's sealed neon-derived implied weight", "domain": "The source-reported sealed comparison, not a new blind test in this drafting round.", "group": null, "hypotheses": [ "Use the s732 vault and the derivation/unseal sequence reported in Paper 9." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 129 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 9", "section": "§6, Remark 6.1: pentagon vault value", "pdf_page": 134, "quote": "The s732 vault held kimplied (20 Ne) = 2.617965, never disclosed; the lane derived T5 = φ2 = 2.618034 from the pentagon identity alone — 26 ppm." }, "caution": "The reported vault match is not a new blind receipt, a global statistical significance or a derivation of the energy interface.", "candidate_ids": [ "C2-077" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-148" }, { "type": "related_to", "target": "LIB2-149" }, { "type": "related_to", "target": "LIB2-144" } ], "url": "/library-v2/LIB2-150/", "content_sha256": "84fd8a730e71b88736dac8de570d6c6d04bc3da5649d4258ddc666aaf8c51936", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-151", "entry_version": 7, "class": "CLAIM", "title": "The suite reports a sealed ninth-weight match", "statement": "The suite reports that T9 = 7 + ϕ⁻⁴ = 7.1459 matched the sealed implied value 7.1385 at 0.10%, rather than taking the linear value 7.", "scope": { "carrier": "The ninth composition weight and its sealed implied counterpart", "domain": "The source-reported second trace-ladder vault match.", "group": null, "hypotheses": [ "Use the s737 answer sheet and the source's scheduled unsealing procedure." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 129 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 9", "section": "§6, Remark 6.1: ninth-weight vault", "pdf_page": 134, "quote": "The s737 answer sheet held the implied T9 = 7.1385 behind the sole hint “at n = 9 the ladder does not do the obvious thing”; the rule declined the linear 7 and produced 7 + φ−4 = 7.1459 — 0.10%, against a vault the lane never saw." }, "caution": "This reported match does not establish a universal forecast rate or certify a new blind result in the library-drafting round.", "candidate_ids": [ "C2-077" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-148" }, { "type": "related_to", "target": "LIB2-149" } ], "url": "/library-v2/LIB2-151/", "content_sha256": "c10d2e187d80dad46dc0b75b9767bfaf17e25e35b220fd14457b4fee089adc6d", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-152", "entry_version": 8, "class": "CLAIM", "title": "The Hoyle excitation passes the source's frozen bar", "statement": "The source's Hoyle excitation (ϕ⁻¹⁵ + ϕ⁻¹⁸)√σ = 0.4033 MeV is compared with 0.3796 MeV, a printed 6.2% difference that passes its frozen 10% bar.", "scope": { "carrier": "The trace-free breathing excitation and its declared energy interface", "domain": "The source-reported Hoyle-state row and its pre-frozen bar.", "group": null, "hypotheses": [ "Use the same triple-alpha associator and the two printed phi powers.", "Import the string-tension scale to express the excitation in MeV." ], "physical_target": "Hoyle excitation above the three-alpha threshold", "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 129 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 9", "section": "§7, Frozen Hoyle bar", "pdf_page": 134, "quote": "Hoyle (scored PASS at the frozen 10% bar, A1354):" }, "caution": "The source-reported pass does not turn the associator into an energy or derive the dimensional scale and full nuclear dynamics.", "candidate_ids": [ "C2-075" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-144" } ], "url": "/library-v2/LIB2-152/", "content_sha256": "2c46de35e5a1238d16bcdd8167e9bdba26ccb92bed35c432ca40f1bf49796a36", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-153", "entry_version": 9, "class": "CLAIM", "title": "The freeze-state ledger records sharp passes and a separately typed obstruction", "statement": "The freeze-state ledger reports seventeen sharp binding-energy passes from deuterium through calcium plus one typed silicon obstruction; its worst untyped residual is 0.77% (³H), and 0.37% is the worst of the A ≥ 5 non-silicon continuation.", "scope": { "carrier": "The freeze-state binding-energy ledger and its stated scoring categories", "domain": "The published aggregate ledger report, not a new rescore or a joint statistical likelihood.", "group": null, "hypotheses": [ "Use the pre-answer bars and the separate silicon refinement-gate disposition printed in Paper 9." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 131 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 9", "section": "§8, Ledger aggregate", "pdf_page": 135, "quote": "That is seventeen sharp passes, deuterium through calcium (worst untyped 0.77%, 3 H; 0.37% is the worst of the A ≥ 5 non-silicon continuation — Rev32.9), plus one typed obstruction (28 Si, 0.334%; pre-answer bar 1% passed, §9)," }, "caution": "The aggregate report is not an independent re-audit, a global likelihood or a completed charge-magnitude and shell model.", "candidate_ids": [ "C2-078" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-145" }, { "type": "related_to", "target": "LIB2-152" }, { "type": "related_to", "target": "LIB2-154" } ], "url": "/library-v2/LIB2-153/", "content_sha256": "b1cbc12f81ebcf94f9d5c7616c824ae19a98b6f17f66716aa45acf8acda8977f", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-154", "entry_version": 10, "class": "CLAIM", "title": "The silicon residual passed its original bar and took the typed-obstruction branch", "statement": "The 28Si first-circulation residual is 0.334%: it passed the pre-answer 1% bar and took the obstruction branch of the later 0.1% refinement gate, so the source counts it as neither a sharp nor a miss.", "scope": { "carrier": "The first-circulation silicon binding residual and its two-stage scoring history", "domain": "The typed residual and its recorded scoring disposition, not the separate three-way readout fork.", "group": null, "hypotheses": [ "Distinguish the pre-answer D1060 bar from the post-answer D1061 refinement gate.", "The obstruction option was in the refinement gate's frozen text before that gate was applied." ], "physical_target": "Silicon first-circulation binding residual", "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 132 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 9", "section": "§9, Original bar and residual", "pdf_page": 136, "quote": "The pre-answer frozen bar for 28 Si was 1% (D1060); the entry passed it at 0.334%." }, "caution": "This disposition neither proves universal irreducibility nor resolves the separate silicon readout fork or packing mechanism.", "candidate_ids": [ "C2-083" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-153" } ], "url": "/library-v2/LIB2-154/", "content_sha256": "be200aa4222125afde9615997e950d427d6f38b4e3e1edfcbbea93407ae9acce", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-155", "entry_version": 13, "class": "CLAIM", "title": "The charge-magnitude ledger retains two exposed proton-separation defects", "statement": "Under the banked baseline ruling, the proton-separation estimate Sp(9B) is 1.29 times the world value and Sp(8B) is 2.60 times the world value; correct signs and counts do not close the magnitude sector.", "scope": { "carrier": "The registered charge-sector proton-separation estimates", "domain": "The exposed charge-magnitude defects, distinct from the binding-energy sharp tally.", "group": null, "hypotheses": [ "Use the banked baseline ruling with the refined daughter ledger.", "Keep configuration-dependent coherence and screening as unresolved mechanisms." ], "physical_target": "Proton-separation-energy magnitude diagnostics", "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 132 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 9", "section": "§9, Charge-magnitude defects", "pdf_page": 137, "quote": "Charge signs and counts are derived; charge magnitudes wander: Sp (9 B) × 1.29, Sp (8 B) × 2.60 under the baseline ruling." }, "caution": "The strong sign/count record does not derive charge magnitudes or justify choosing a more favourable baseline after comparison.", "candidate_ids": [ "C2-072" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-153" } ], "url": "/library-v2/LIB2-155/", "content_sha256": "eac25a1b4beac5273157b388db70baf667881c594300a9b30c770fe5fb654e80", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-156", "entry_version": 8, "class": "CLAIM", "title": "The direct Markov-second-moment repair has the wrong sign", "statement": "The canonical connected Markov second moment is non-negative, while the required binding correction at n = 6,7 is negative; the declared direct second-moment repair lacks the negative energy coefficient needed to reverse the sign.", "scope": { "carrier": "The connected normalized Markov second moment in Aφ = ATLφ/⟨f4⟩", "domain": "The direct second-moment binding-repair class, not all possible energy attachments.", "group": null, "hypotheses": [ "Use the canonical connected normalized Markov second moment of the registered mirror-odd circulation.", "The required correction is the source's negative six-to-seven-cell deficit." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 131 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Paper 9", "section": "§9, Direct annular second-moment attachment", "pdf_page": 136, "quote": "the canonical connected Markov second moment is non-negative, whereas the required n = 6, 7 binding correction is negative, so the annular order does not derive the negative energy coefficient that would reverse the sign;" }, "caution": "This excludes the declared direct attachment, not every annular operator or an independently derived negative energy map.", "candidate_ids": [ "C2-083", "C2-128" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-154" }, { "type": "related_to", "target": "LIB2-144" } ], "url": "/library-v2/LIB2-156/", "content_sha256": "4e0b4dc922aefbdd89a4fb49603b6465f655450c474a28bbd613f20405e623d8", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-157", "entry_version": 7, "class": "CLAIM", "title": "The connected second moment does not switch off at the later cells", "statement": "The ribbon full-twist identity leaves the registered connected Markov second moment strictly positive at n = 8,9,10, excluding exact switch-off there.", "scope": { "carrier": "The connected normalized Markov second moment of the registered annular circulation", "domain": "Exact switch-off at the stated cells, distinct from the unscored finite support threshold.", "group": null, "hypotheses": [ "Use the ribbon full-twist identity and connected moment specified in Paper 9 §9." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 131 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Paper 9", "section": "§9, Ribbon full-twist obstruction", "pdf_page": 136, "quote": "full-twist identity also excludes exact switch-off (Ωn > 0 at n = 8, 9, 10)." }, "caution": "Nonzero later moments do not settle the finite support-threshold test, whose energy coefficient remains open.", "candidate_ids": [ "C2-083", "C2-128" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-156" }, { "type": "related_to", "target": "LIB2-154" } ], "url": "/library-v2/LIB2-157/", "content_sha256": "3cc1e5f02dd8c002995c08c26602ae182f515feefc3039be889b5ee63fa1d920", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-158", "entry_version": 11, "class": "CLAIM", "title": "The tested perturbative annular attachment does not explain the deficit window", "statement": "The tested clock/twist and total-charge-resolved fusion-path constructions do not supply the {6,7} deficit window; the registered perturbative annular attachment remains closed negative.", "scope": { "carrier": "The registered clock/twist candidates and charge-resolved Fibonacci fusion-path representation", "domain": "The declared perturbative annular-repair candidates only.", "group": null, "hypotheses": [ "Use the clock-factor and fusion-path tests reported in Paper 9 §9.", "Keep the six-to-seven-cell deficit distinct from the separate silicon readout fork." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 131 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Paper 9", "section": "§9, Perturbative annular disposition", "pdf_page": 136, "quote": "the perturbative annular attachment is closed negative as well (A1545);" }, "caution": "The tested annular failures do not exclude the separately named packing/coordination class or constitute a universal annular no-go.", "candidate_ids": [ "C2-083", "C2-128" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-156" }, { "type": "related_to", "target": "LIB2-157" }, { "type": "related_to", "target": "LIB2-154" } ], "url": "/library-v2/LIB2-158/", "content_sha256": "8ad72a74a467befc60e420f242276a7f77aa814256bc899134471c7f13b7da5d", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-159", "entry_version": 10, "class": "CLAIM", "title": "The separate silicon readout remains a three-way fork", "statement": "The separate 28Si readout admits amplitude +1.457939×10⁻⁶, probability +2.524367×10⁻⁴ and a nonselective depth-15 channel; the unchanged 40Ca control is −3.172350×10⁻⁴.", "scope": { "carrier": "The separate silicon readout of the N1–N5 campaign and its unchanged calcium control", "domain": "The three alternative readouts, not a corrected binding-energy ledger entry.", "group": null, "hypotheses": [ "Keep amplitude (φ−5), probability (φ−10) and nonselective depth-15 readings distinct.", "Retain the common calcium control alongside the fork." ], "physical_target": "The separate silicon readout and calcium control", "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 132 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 9", "section": "§9, Separate readout campaign", "pdf_page": 137, "quote": "a readout for 28 Si that is not the 0.334% first-circulation binding residual discussed in this section." }, "caution": "No branch is selected, and this fork is not the separately scored first-circulation binding residual.", "candidate_ids": [ "C2-083" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-154" } ], "url": "/library-v2/LIB2-159/", "content_sha256": "e7c45d23e7d00ce5c9d779839cf00eae4f829a09b14c29bdab364000e7116982", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-160", "entry_version": 12, "class": "CLAIM", "title": "The fixed-Z isospin coefficient is selected rather than derived", "statement": "The isospin Casimir coefficient χ = ϕ⁻⁶T3 is selected on the fixed-Z chains, not derived; the source carries the sector as loaded.", "scope": { "carrier": "The fixed-Z isospin Casimir term in the nuclear ledger", "domain": "The selected coefficient and its declared loaded status.", "group": null, "hypotheses": [ "Use the fixed-Z chain selection reported in the source." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 133 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Paper 9", "section": "§9, Isospin coefficient", "pdf_page": 138, "quote": "The isospin Casimir coefficient χ = φ−6 T3 is selected on the fixed-Z chains, not derived." }, "caution": "The selected coefficient is not a derived isospin magnitude law or a prediction of the neutron–proton mass difference.", "candidate_ids": [ "C2-129" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-155" } ], "url": "/library-v2/LIB2-160/", "content_sha256": "0c7fdf9ef60393342eb1f1be32b2cfc74ef451732f6ff46b82e32bb835b6bfbf", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-161", "entry_version": 11, "class": "CLAIM", "title": "The registered up–down operation is a parity, not a derived isospin action", "statement": "The registered u ↔ d operation is the split-octonion sign map e7 → −e7, exchanging Hu and Hd as a Z2 parity rather than a derived SU(2) action.", "scope": { "carrier": "The split-octonion sign map e7 → −e7 on the loaded up/down Higgs dictionary", "domain": "The registered up–down operation, not a derived nuclear SU(2) dynamics.", "group": null, "hypotheses": [ "Use the A689 field dictionary and its registered sign map (read literally, the flip of e7 alone; neither it nor full conjugation is a Jordan automorphism)." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 133 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Paper 9", "section": "§9, Registered up–down operation", "pdf_page": 138, "quote": "The only registered u ↔ d object is the Os sign map e7 → −e7 (Hu ↔ Hd ; A689 dictionary; read literally, the flip of e7 alone — s1170 shows the phrase also fits full conjugation, and neither map is a Jordan automorphism) — a Z2 parity, not an SU (2)" }, "caution": "The parity does not construct a continuous isospin action or supply the missing QCD flip energy.", "candidate_ids": [ "C2-129" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-160" }, { "type": "related_to", "target": "LIB2-108" } ], "url": "/library-v2/LIB2-161/", "content_sha256": "1da0dbf7e4438d88577deeb9f05db0ff19c0a064c9a29c7379060101bf1123ef", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-162", "entry_version": 8, "class": "CLAIM", "title": "The registered breathing weight is mirror-even and charge-blind", "statement": "The registered trace-free breathing excitation of the alpha-plus-three-body bridge has weight Δbr = ϕ⁻¹⁵ − ϕ⁻¹⁸ and is mirror-even and charge-blind.", "scope": { "carrier": "The trace-free breathing generator in the frozen cluster menu", "domain": "The typed breathing weight, distinct from the Hoyle comparison and its energy interface.", "group": null, "hypotheses": [ "Use the registered bridge typing and the existing triangle/heptad and annulus weights." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 130 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 9", "section": "§7, Breathing-kernel typing", "pdf_page": 134, "quote": "The breathing kernel (A1357): the same object, typed — the trace-free breathing excitation of the α + 3-body bridge, mirror-even and charge-blind, priced by" }, "caution": "The weight does not determine whether the excitation occurs in every parent typing; the A = 8 accounting remains open.", "candidate_ids": [ "C2-073", "C2-075" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-143" }, { "type": "related_to", "target": "LIB2-152" }, { "type": "related_to", "target": "LIB2-144" } ], "url": "/library-v2/LIB2-162/", "content_sha256": "e79529b00eb34fe0e4d74e597976bd28e4a144f399bb8b8f8dbb9efd07191f68", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-163", "entry_version": 9, "class": "CLAIM", "title": "The separation-energy rule uses the refined daughter ledger", "statement": "The banked separation-energy rule is Sx(P → D + x) = B(P) − B(Dledger) − B(x), with the refined daughter always and B(x) = 0 for a single emitted nucleon; neutral excitations cancel only when present in both typings.", "scope": { "carrier": "Parent and refined daughter objects in the cluster ledger", "domain": "The declared separation-energy bookkeeping rule.", "group": null, "hypotheses": [ "Use the refined daughter ledger rather than switching to a different daughter baseline after comparison." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 130 }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 9", "section": "§7, Banked baseline ruling", "pdf_page": 134, "quote": "Sx (P → D + x) = B(P ) − B(Dledger ) − B(x) with the refined daughter always, where B(x) = 0 for a single emitted nucleon (the case the ruling was banked for) and the bound-fragment term is required otherwise (8 Be→ αα gives 0 at leading order only with it; Rev32.9, A1674 F01; Rev32.10, A1714-F01 — this does not license the open A = 8 alternative baseline)" }, "caution": "The convention does not supply the missing parent-excitation typing or resolve the exposed charge-magnitude defects.", "candidate_ids": [ "C2-072" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-155" }, { "type": "related_to", "target": "LIB2-162" } ], "url": "/library-v2/LIB2-163/", "content_sha256": "82c9e8ca922fd5737d5301798a0e35d47d5484f7098d8bc023771e8b2705fccd", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-164", "entry_version": 8, "class": "CLAIM", "title": "The draft glueball pair falls in the two printed frozen bands", "statement": "At draft tier, the glueball pair has m(0⁺⁺)/√σ = 3.4777 in [3.3,3.9] and m(2⁺⁺)/m(0⁺⁺) = √2 in [1.3,1.6].", "scope": { "carrier": "The draft vacuum-normalized annulus-correlator glueball construction", "domain": "The two source-printed dimensionless readouts and frozen bands.", "group": null, "hypotheses": [ "Use the registered annulus saddle and correlator normalization." ], "physical_target": "Dimensionless glueball pair", "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 131 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 9", "section": "Table 1, Glueball pair", "pdf_page": 135, "quote": "m(0++ )/ σ √8π log φ = 3.4777 in band [3.3, 3.9] m(2++ )/m(0++ ) 2 in band [1.3, 1.6]" }, "caution": "The band matches are draft-tier source reports, not a continuum Yang–Mills construction or an absolute glueball-scale derivation.", "candidate_ids": [ "C2-078", "C2-099" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-153" } ], "url": "/library-v2/LIB2-164/", "content_sha256": "cd10a66eeab4496f8a869b3b99c34210d7c8558eb98ea08c6f2c058a3b325caf", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-165", "entry_version": 8, "class": "CLAIM", "title": "The finite Gaussian OS subgate is reported as a conditional checkpoint", "statement": "The source reports a finite Gaussian Osterwalder–Schrader subgate pass at conditional/finite tier, not a reflection-positive continuum construction.", "scope": { "carrier": "The finite Gaussian checkpoint reported in the continuum staging map", "domain": "The finite OS subgate only, distinct from the toy resolvent and the Cartan-regulator state.", "group": null, "hypotheses": [ "Use the finite Gaussian construction and conditions referred to in the source; their detailed payload is not supplied." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 171 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix E", "section": "§8, First finite OS subgate", "pdf_page": 178, "quote": "The continuum frontier moved by one typed step: the first finite Gaussian OS subgate pass and a toy resolvent, both two-host byte-certified (A1529), are recorded at conditional/finite tier" }, "caution": "The finite subgate does not establish a continuum limit, a reflection-positive continuum measure, an interacting pole or LSZ.", "candidate_ids": [ "C2-119" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-021" } ], "url": "/library-v2/LIB2-165/", "content_sha256": "f9cf69650a521b9636b4e083aba38a267d13d4cd5097e0f18a33c444f8b4ef95", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-166", "entry_version": 7, "class": "CLAIM", "title": "The toy resolvent remains a finite conditional checkpoint", "statement": "The toy resolvent accompanying the Gaussian subgate is source-reported as two-host byte-certified at conditional/finite tier.", "scope": { "carrier": "The toy resolvent in the source's finite continuum-staging checkpoint", "domain": "The reported finite resolvent, not a continuum two-point function.", "group": null, "hypotheses": [ "Use the particular toy construction referred to by A1529; the suite passage gives no full operator formula." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 171 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix E", "section": "§8, Toy resolvent checkpoint", "pdf_page": 178, "quote": "The continuum frontier moved by one typed step: the first finite Gaussian OS subgate pass and a toy resolvent, both two-host byte-certified (A1529), are recorded at conditional/finite tier" }, "caution": "The toy resolvent does not constitute an interacting physical propagator, a pole theorem or an LSZ construction.", "candidate_ids": [ "C2-119" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-165" } ], "url": "/library-v2/LIB2-166/", "content_sha256": "f6f9ee2598b69eae0c8ce459bf68847aa014ef2eee22795be88628082b380d88", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-167", "entry_version": 12, "class": "CLAIM", "title": "The motivated clock seed is extra structure, not an energy order of tensor layers", "statement": "The motivated clock generator Hclk is extra Cartan structure on the symplectic carrier, compatible with the absence of a derived tensor-layer energy order; the golden bridge corroborates a face of its flow but does not derive the seed.", "scope": { "carrier": "The symplectic clock/dynamics seed and the distinct tensor-layer order structure", "domain": "The printed compatibility and corroboration statement.", "group": null, "hypotheses": [ "Retain the extra Cartan grading rather than interpreting it as a tensor-layer order." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 350 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix X", "section": "§3.5, No-energy-order fence", "pdf_page": 371, "quote": "The A1489 order theorems stand: the ⊗-layers carry no derived energy order." }, "caution": "The motivated seed does not derive measured time, a physical energy ordering, masses or the missing continuum functor.", "candidate_ids": [ "C2-123", "C2-154" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-015" } ], "url": "/library-v2/LIB2-167/", "content_sha256": "c0735612cfbbfb16ec0b070b0d1b9477ca6bbefa94da288b5ee77f5881907da8", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-168", "entry_version": 8, "class": "CLAIM", "title": "The trace-built MacDowell–Mansouri action is a signature-sector candidate", "statement": "The trace-built MacDowell–Mansouri action is a candidate parent for the signature/Cartan sector, yielding Einstein–Hilbert plus a cosmological term after the Euler discard.", "scope": { "carrier": "The Cartan/signature-sector traces and curvature form", "domain": "The form-calculus action for the named sector only.", "group": null, "hypotheses": [ "Use the trace-derived metric and orientation of Proposition 5.3 and the action convention of Named datum 5.4.", "The scale registration and dimensionless coupling remain separately priced." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 303 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "analytic", "availability": "shipped" }, { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix T", "section": "§5, Named datum 5.4: candidate action", "pdf_page": 320, "quote": "The signature-sector parent action — candidate" }, "caution": "This candidate is not the full particle, generation, gauge or mass action and does not restore the rejected parent-action route.", "candidate_ids": [ "C2-091" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-168/", "content_sha256": "9de858e717581798e4ec7494a1a91bc2e62f2ebb7673a96efe8b4d4a0cf3899f", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-169", "entry_version": 7, "class": "CLAIM", "title": "The Euclidean MM/EH action has the stated conformal instability", "statement": "The Euclidean MacDowell–Mansouri/Einstein–Hilbert action is unbounded below in the conformal direction in the registered convention.", "scope": { "carrier": "The Euclidean MM/EH action under conformal variation", "domain": "The stated conformal direction and sign convention, not every regulated gravitational measure.", "group": null, "hypotheses": [ "Use the source's conformal parametrization and MM/EH sign convention." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 304 }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix T", "section": "§6, Theorem 6.7: conformal-mode obstruction", "pdf_page": 321, "quote": "the Euclidean MM/EH action is unbounded below in the conformal direction" }, "caution": "This sign obstruction does not exclude regulated positive measures or a constrained completion outside the pure weight.", "candidate_ids": [ "C2-086" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-168" } ], "url": "/library-v2/LIB2-169/", "content_sha256": "5eb73e0c40aebc1bc81e7be15a29c11f2df3373609e12a8ab69da0dc4e737b00", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-170", "entry_version": 9, "class": "CLAIM", "title": "A reflection-positive Cartan state exists at finite regulator", "statement": "The registered heat-kernel × Haar product on Spin(5) edges gives a normalized reflection-positive state, an OS Hilbert space and a positive transfer operator at finite regulator.", "scope": { "carrier": "The finite Cartan regulator with a heat-kernel × Haar edge measure", "domain": "Finite-regulator state, OS Hilbert space and transfer operator only.", "group": "Spin(5)", "hypotheses": [ "Use the registered compact Spin(5) edge measure, crossing split and nonnegative Peter–Weyl coefficients." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 305 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" }, { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix T", "section": "§7, Named datum 7.1: finite state", "pdf_page": 321, "quote": "A normalized reflection-positive state exists at the finite Cartan regulator tier: a heat-kernel × Haar product on Spin(5) edges," }, "caution": "Finite-regulator existence does not establish the continuum limit, Einstein universality or a selected coherent boundary state.", "candidate_ids": [ "C2-094" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-169" }, { "type": "rests_on_premise", "target": "PRM-014" } ], "url": "/library-v2/LIB2-170/", "content_sha256": "ac55344f3cc1cf8beb5682b46536fc148025bb9beec04402f6915b2d03206195", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-171", "entry_version": 7, "class": "CLAIM", "title": "The pure MacDowell–Mansouri quadratic form is not a positive covariance", "statement": "On the registered 16-representation, BMM = tr(ΓTI TJ) has inertia (3,3,4), so the pure MM/EH weight cannot be a positive coercive covariance.", "scope": { "carrier": "The MacDowell–Mansouri quadratic form on the registered generator space", "domain": "The pure MM/EH quadratic form, distinct from the positive completion cone.", "group": null, "hypotheses": [ "Use the registered 16-representation, generators and chirality trace." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 305 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix T", "section": "§7, Theorem 7.3: representation and quadratic form", "pdf_page": 322, "quote": "On the 16-representation, BC = −tr(TI TJ ) = 4I10 exactly, inertia (10, 0); BMM = tr(ΓTI TJ ) has characteristic polynomial" }, "caution": "This finite-algebraic obstruction does not exclude the positive completion family or prove that a finite Cartan state is Einstein gravity.", "candidate_ids": [ "C2-095" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-169" }, { "type": "related_to", "target": "LIB2-170" } ], "url": "/library-v2/LIB2-171/", "content_sha256": "2313fcbd2ca764d9b3189c4415bac3c4a55b69620258cc98289d42853b6070f3", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-172", "entry_version": 11, "class": "CLAIM", "title": "The positive completion cone has a strict coefficient domain", "statement": "The registered quadratic completion Bα,β = αBC + βBMM is positive definite exactly when α > 0 and |β| < α; its nonzero boundary α = |β| > 0 is chiral-null, and the apex α = β = 0 is the zero form.", "scope": { "carrier": "The two-parameter completion of the Cartan and MacDowell–Mansouri quadratic forms", "domain": "The displayed quadratic completion, not an established nonlinear gravitational continuum measure.", "group": null, "hypotheses": [ "Use the forms BC and BMM on the registered generator space." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 305 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "analytic", "availability": "shipped" } ], "primary_source": { "component": "Appendix T", "section": "§7, Proposition 7.4: positive completion cone", "pdf_page": 322, "quote": "Bα,β = αBC + βBMM > 0 ⇐⇒ α > 0, |β| < α," }, "caution": "Positive quadratic completion does not establish Einstein universality, a continuum limit or generic nonlinear reflection positivity.", "candidate_ids": [ "C2-095" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-171" }, { "type": "related_to", "target": "LIB2-170" } ], "url": "/library-v2/LIB2-172/", "content_sha256": "91828e8945db9d78f87ad5e225f26c3868ea1fa19e51eef5088bc8129f2a9579", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-173", "entry_version": 7, "class": "CLAIM", "title": "The ordered state pair supplies the additive relative modular score", "statement": "For the registered ordered golden state pair, the additive half-log score is Krel = Dϕ = diag(1,0,−1) on the golden lattice.", "scope": { "carrier": "The ordered golden state pair and its relative modular score", "domain": "The score associated with the supplied state pair, not a natural point of the bare module.", "group": null, "hypotheses": [ "Use the ordered state pair of Theorem 10.1 and its additivity premise." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 309 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix T", "section": "§10, Theorem 10.1: half-log score", "pdf_page": 326, "quote": "the half-log score is diag(1, 0, −1) on the golden lattice: Krel = Dφ ." }, "caution": "The score does not intrinsically select the ordered state pair or construct the microscopic mass/generation readout.", "candidate_ids": [ "C2-093" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "rests_on_premise", "target": "PRM-005" } ], "url": "/library-v2/LIB2-173/", "content_sha256": "761686913f82c21c86503a16372cc83457199e28aa72502e45e97dbc6529998b", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-174", "entry_version": 11, "class": "CLAIM", "title": "The record-quotient observation composite is unique under its seven premises", "statement": "The record-quotient functor OMOS is unique without a continuous modulus under additivity, unitality, minimality, Pin typing, OS typing, isometry and a whitened source; the microscopic theory has not selected it.", "scope": { "carrier": "The ordered-state to record-quotient observation composite", "domain": "The ordered-state / record-quotient functor, not the distinct microscopic mass/generation observation map.", "group": null, "hypotheses": [ "Require additivity, unitality, minimality, Pin typing, OS typing, isometry and the whitened source.", "Use the registered ordered state pair and its modular score." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 309 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix T", "section": "§10, Named datum 10.7: composite and premises", "pdf_page": 327, "quote": "The composite — ordered state pair → modular score → unital-CP normalized readout → minimal dilation → Pin/OS-even spectral calculus — is unique under seven premises, each with a verified countermodel showing it has teeth: additivity, unitality, minimality, Pin typing, OS typing, isometry, and the whitened source." }, "caution": "This construction does not select a microscopic realization, restore excluded support or build the distinct mass/generation observation map.", "candidate_ids": [ "C2-093" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "depends_on", "target": "LIB2-173" } ], "url": "/library-v2/LIB2-174/", "content_sha256": "071a5ada6acf918804479ecf23ba4fda8cc63e3f2f3b0cb4600af868cbecb059", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-175", "entry_version": 12, "class": "CLAIM", "title": "The supported MOS quotient has rank three and relative rank two", "statement": "The supported observation quotient ΠMOS has rank 3 and relative rank 2 < 5; it is not the full microscopic loading.", "scope": { "carrier": "The supported MOS observation quotient from paired and annular carriers", "domain": "The finite supported quotient, not the microscopic support-restoring map.", "group": null, "hypotheses": [ "Use the registered pair coisometry, Hodge frame and annular Fourier support." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 310 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix T", "section": "§11, Theorem 11.2: partial isometry", "pdf_page": 328, "quote": "exact partial isometry (Π̃Π̃T = Pann , Π̃T Π̃ = PV4 ) killing all pair-difference modes;" }, "caution": "The finite quotient does not restore missing microscopic modes or discharge the full observation-map construction.", "candidate_ids": [ "C2-092" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-174" } ], "url": "/library-v2/LIB2-175/", "content_sha256": "add96a1abbf9ad86a08030c878f8f28cd98e63ae1f3d007652bfead8b9048c46", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-176", "entry_version": 9, "class": "CLAIM", "title": "History, character and boundary record are one registered record type", "statement": "In the OMOS record process, history, character and boundary record describe one object: squared branch norms equal cylinder probabilities and distinct histories are orthogonal.", "scope": { "carrier": "The classical record process derived from the record-quotient functor", "domain": "Equivalence of the record descriptions, not selection of a particular realized history.", "group": null, "hypotheses": [ "Use the registered transition process, record isometry and compatible finite-stage characters." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 310 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix T", "section": "§12, Theorem 12.1: record isometry", "pdf_page": 329, "quote": "squared branch norms equal cylinder probabilities (Rev32.9, A1677 F01); and distinct histories are orthogonal — a strongly decoherent classical record process derived from OMOS ." }, "caution": "The equivalence of record descriptions does not determine which particular history is realized.", "candidate_ids": [ "C2-085" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "depends_on", "target": "LIB2-174" } ], "url": "/library-v2/LIB2-176/", "content_sha256": "de3bf8de12c033ebe21563d9d7f47c271cba0f17fece8460297fcc3fe0366601", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-177", "entry_version": 10, "class": "CLAIM", "title": "The realized history is sample data rather than a value selected by its law", "statement": "The realized history is sample/record data not determined by its law; constructing the record law and type does not select the particular realized value.", "scope": { "carrier": "The realized value of the registered stochastic record process", "domain": "The law/value distinction in this record process.", "group": null, "hypotheses": [ "Use the registered Markov-kernel law and distinguish it from a realized sample." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 311 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix T", "section": "§12, Actuality status split", "pdf_page": 329, "quote": "Xrealized-value = not determined by the law — it is sample/record data, by theorem." }, "caution": "This typing does not predict the specific realized outcome or remove the source's separate conserved-sector and history-candidate conditions.", "candidate_ids": [ "C2-085" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-176" } ], "url": "/library-v2/LIB2-177/", "content_sha256": "200ba66b73bfad5a974ecff95aead8f215c1a01ff15bf65b39753b09cbd200bb", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-178", "entry_version": 9, "class": "CLAIM", "title": "The locked basepoint census has no qualifying intrinsic datum", "statement": "In the locked census of 30 candidates, the 5 intrinsic rows supply no intrinsic datum with a nonzero stabilizer-fixed vector; face 2 is recorded as Definitional at the shipped registered tiers.", "scope": { "carrier": "The locked candidate universe for intrinsic shell basepoint selection", "domain": "The bounded face-2 census, not a universal nonexistence theorem for intrinsic selectors.", "group": null, "hypotheses": [ "Restrict to the thirty-row shipped registered candidate universe.", "Require the intrinsic datum to have a nonzero stabilizer-fixed vector." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 315 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix T", "section": "§15.1, Dated face-2 amendment", "pdf_page": 333, "quote": "Face 2 is now Definitional at every shipped registered tier: the locked census found 30 candidate rows, 5 intrinsic rows and no intrinsic datum with a nonzero stabilizer-fixed vector." }, "caution": "The bounded census does not rule out an independently derived subgroup outside the shipped inventory or turn a transported point into an intrinsic choice.", "candidate_ids": [ "C2-133" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-012" }, { "type": "related_to", "target": "LIB2-005" } ], "url": "/library-v2/LIB2-178/", "content_sha256": "9fbe11d1e5933a23379f5fc539446cb36b4e0b385a0727b43a6ef88f2f00e16c", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-179", "entry_version": 7, "class": "CLAIM", "title": "The registered stabilizer has no nonzero invariant odd covector", "statement": "The largest registered stabilizer subgroup preserving J− has no nonzero invariant covector on J−, blocking the attempted invariant scalar row.", "scope": { "carrier": "The odd Albert sector and the largest registered stabilizer preserving it", "domain": "The invariant-covector attempt, not the state-dependent covariant successor.", "group": null, "hypotheses": [ "Use the stabilizer and invariant scalar-row requirement of Appendix T §15.2." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 316 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix T", "section": "§15.2, Invariant scalar-row attempt", "pdf_page": 334, "quote": "The first attempt demanded an invariant scalar row ℓodd : J− → R." }, "caution": "The invariant-row obstruction does not exclude a state-dependent covariant response or determine its physical normalization.", "candidate_ids": [ "C2-134" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-179/", "content_sha256": "f7c88f241838fe785711f6e3f18a1b39d9c15ce04414775755b174665be20e44", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-180", "entry_version": 8, "class": "CLAIM", "title": "The transported A689 grading has trivial rather than alternating character", "statement": "The transported A689 split-norm Z2 grading carries the trivial, not alternating, S3 character, so its direct identification with Hsgn is closed negative.", "scope": { "carrier": "The transported multiplicative grading and the Hermitian sign-character line", "domain": "The direct grading-to-sign-line shortcut, not every possible odd response.", "group": null, "hypotheses": [ "Use the registered A689 grading and its transported S3 action." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 316 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix T", "section": "§15.2, Grading character", "pdf_page": 334, "quote": "the A689 split-norm Z2 was computed to carry the trivial, not the alternating, S3 character [A1556]." }, "caution": "This character mismatch does not eliminate covariant source-character intertwiners or select an endpoint orientation.", "candidate_ids": [ "C2-134" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-179" } ], "url": "/library-v2/LIB2-180/", "content_sha256": "f6682a9f7eb0bd07e781c0ec7ec7ad488994ffc8d63b0689c8a5c82d2b720907", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-181", "entry_version": 8, "class": "CLAIM", "title": "The local covariant odd response is one orbit with an unselected torsor", "statement": "On the transported paired-shell space, HomS3(J−,sgn) has real dimension 4; its normalized sphere is one connected-covariance orbit, leaving the endpoint-exchange torsor τ = ±1 unselected.", "scope": { "carrier": "The transported paired-shell generation space and its odd source-character intertwiners", "domain": "The local response class at the transported point, not a selected microscopic readout.", "group": null, "hypotheses": [ "Use the transported pointed carrier and the connected covariance-group equivalence.", "Normalize the source intertwiner without choosing an endpoint-exchange side." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 316 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix T", "section": "§15.2, Source-intertwiner space and covariance orbit", "pdf_page": 334, "quote": "On the transported paired-shell generation space G6 , the source intertwiner space HomS3 (J− , sgn) has real dimension four, while its normalized sphere is a single orbit of the connected covariance group." }, "caution": "A single equivalence class is not a selected representative, endpoint orientation or physical response coefficient.", "candidate_ids": [ "C2-134" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-013" }, { "type": "related_to", "target": "LIB2-179" }, { "type": "related_to", "target": "LIB2-180" } ], "url": "/library-v2/LIB2-181/", "content_sha256": "5881646a8c47d2549361508da35526323da880c02d5f5bd1ccbf59bf5a6c354f", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-182", "entry_version": 9, "class": "CLAIM", "title": "The MOS channel family permits a range of odd-response amplitudes", "statement": "At record-quotient tier, the unital completely positive channel Wλ,τ exists for |λ| ≤ √2 and reproduces the local odd leg at |λ| = √2; whitening does not force that endpoint.", "scope": { "carrier": "The registered unital completely positive record-quotient channel", "domain": "The channel family and its endpoint, not a selected microscopic amplitude.", "group": null, "hypotheses": [ "Use the registered source whitening, covariance, zero-effect and torsor properties." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 316 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix T", "section": "§15.3, Record-quotient channel existence", "pdf_page": 334, "quote": "At record-quotient tier a unital completely positive channel exists," }, "caution": "Complete positivity and whitening do not select the endpoint or provide a microscopic support-restoring observation map.", "candidate_ids": [ "C2-135" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-181" }, { "type": "related_to", "target": "LIB2-175" } ], "url": "/library-v2/LIB2-182/", "content_sha256": "b6fc3e1b5faa410ea900cad2a202eb7cfee4015a5add17f71b7f4b271a2f5bfb", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-183", "entry_version": 9, "class": "CLAIM", "title": "The reversal-covariant score solder bounds the product response", "statement": "The registered reversal-covariant score solder Ξ: C*(Dϕ) ≅ C³ → M2(C) has |µ| ≤ 1, so its response with the MOS channel obeys |λµ| ≤ √2.", "scope": { "carrier": "The score solder from the ordered-score algebra to the source matrix algebra", "domain": "The score-solder and product bounds, not a chosen normalization.", "group": null, "hypotheses": [ "Use the reversal-covariant score solder of A1559.", "Combine it with the registered MOS channel bound on λ." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 316 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix T", "section": "§15.3, Reversal-covariant score solder", "pdf_page": 334, "quote": "The reversal-covariant score solder" }, "caution": "The product bound does not force a unit response or close the distinct microscopic observation and normalization problems.", "candidate_ids": [ "C2-135" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "depends_on", "target": "LIB2-182" } ], "url": "/library-v2/LIB2-183/", "content_sha256": "08508166cd4033cb7e4af9e8083dbd3fc08a00f9ccc1b158da58ec66757a5e5a", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-184", "entry_version": 12, "class": "CLAIM", "title": "The registered normalization census contains no forcing row", "statement": "The complete registered normalization census grew from 28 to 40 typed rows with zero forcing rows; none of the banked conditions fixes |λµ|.", "scope": { "carrier": "The registered normalization conditions for the MOS channel and score solder", "domain": "The closed registered census, not a universal exclusion of future microscopic normalization laws.", "group": null, "hypotheses": [ "Restrict to the supplied normalization inventory and the tiers reached by its package." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 316 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix T", "section": "§15.3, Normalization-census result", "pdf_page": 334, "quote": "the complete registered normalization census grew from 28 to 40 typed rows with zero forcing rows [A1559,A1560]." }, "caution": "The census does not exclude a new microscopic support-restoring map or make the adopted normalization a theorem.", "candidate_ids": [ "C2-135" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-182" }, { "type": "related_to", "target": "LIB2-183" } ], "url": "/library-v2/LIB2-184/", "content_sha256": "2f35857180d84f663881676f1b8487886fbd15fd5dac3b2cad4c09e0282b15ea", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-185", "entry_version": 8, "class": "CLAIM", "title": "The rank-two support certificate excludes a rank-five extension at the MOS tier", "statement": "An ambient rank-5 extension exists, but the record-support condition excludes it at the printed MOS tier by an exact rank-two support certificate.", "scope": { "carrier": "The record-support constraint and an ambient linear-algebra extension", "domain": "The tier-local support obstruction, not nonexistence of the ambient extension.", "group": null, "hypotheses": [ "Retain the record-support condition of the printed MOS quotient tier." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 316 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix T", "section": "§15.3, Ambient extension and tier-local obstruction", "pdf_page": 334, "quote": "A rank-5 extension exists as ambient linear algebra, but the record-support condition forbids it at the printed MOS tier by an exact rank-two support certificate [A1560]." }, "caution": "The support certificate does not exclude a microscopic map outside the printed quotient tier or deny the ambient rank-five construction.", "candidate_ids": [ "C2-135" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-175" }, { "type": "related_to", "target": "LIB2-184" } ], "url": "/library-v2/LIB2-185/", "content_sha256": "a753bba79e682b499380b8ab998465a50b357e5d1efcc911197d6d7723d0379c", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-186", "entry_version": 8, "class": "CLAIM", "title": "The unit grade-four response is a declared premise", "statement": "PREMISE-GRADE-4-RESPONSE fixes |λµ| = 1 on the transported record quotient and removes its positive amplitude modulus while leaving τ = ±1 unselected.", "scope": { "carrier": "The transported record-quotient response and its declared amplitude identification", "domain": "The chosen quotient-tier premise, not a normalization derived from the microscopic theory.", "group": null, "hypotheses": [ "Adopt the PI-declared identification with the registered unit grade-four carrier response." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 317 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix T", "section": "§15.4, Grade-four response premise", "pdf_page": 335, "quote": "PREMISE-GRADE-4-RESPONSE [A1560; declared S300]. On the transported record-quotient response, identify the normalized score response with the registered unit grade-four carrier response, fixing |λµ| = 1." }, "caution": "The premise does not construct Πfull, prove a microscopic grade-four readout, select the torsor side or derive a CKM quantity.", "candidate_ids": [ "C2-131" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-184" }, { "type": "related_to", "target": "LIB2-183" } ], "url": "/library-v2/LIB2-186/", "content_sha256": "d1087b0d8079ffde80cbf9572979ff0a1bc145618c4ffadd2f7f8cb84b191f14", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-187", "entry_version": 8, "class": "CLAIM", "title": "The unadopted response alternatives retain distinct meanings", "statement": "PREMISE-UNIT-RESPONSE would impose |λµ| = √2, whereas DECLINED imposes no quotient-tier response-isometry premise and leaves |λµ| ≤ √2 with one continuous magnitude; neither alternative was adopted.", "scope": { "carrier": "The two unadopted alternatives to the unit grade-four response premise", "domain": "The stated alternative premises, not two additional chosen physical models.", "group": null, "hypotheses": [ "Use the source's A1560 three-box menu and keep the two alternative meanings distinct." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 317 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix T", "section": "§15.4, Unit-response isometry alternative", "pdf_page": 335, "quote": "RESPONSE (the cross-object isometry ∥Dφ ∥HS = |λµ| ∥Hsgn ∥HS , hence |λµ| = 2, the D1238 leg" }, "caution": "Neither alternative enters the physical spectral-pair gate, and declining an isometry premise does not fix the response to zero.", "candidate_ids": [ "C2-131" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-186" }, { "type": "related_to", "target": "LIB2-183" } ], "url": "/library-v2/LIB2-187/", "content_sha256": "6f4b1409acd27695434b54185a705cdc902788585329989b11f93de0176e7052", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-188", "entry_version": 7, "class": "CLAIM", "title": "The registered free quaternionic fermion determinant is non-negative", "statement": "On the registered orthonormalized branch module, det(mI + D) = m⁸(m² + 3)⁸ gives the source's free quaternionic fermion positivity.", "scope": { "carrier": "The free quaternionic fermion operator on the h-orthonormalized branch module", "domain": "The specified free fermion measure, not a generic interacting chiral measure.", "group": null, "hypotheses": [ "Use the source's real symmetric Euclidean gammas and quaternionic commutant commuting with Dfree." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 305 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix T", "section": "§7, Proposition 7.5: free determinant", "pdf_page": 322, "quote": "the quaternion commutant units commute with Dfree , and det(mI + D) = m8 (m2 + 3)8 exactly" }, "caution": "This free-sector result does not construct the required interacting chiral determinant-line trivialization.", "candidate_ids": [ "C2-094" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-170" }, { "type": "related_to", "target": "LIB2-109" } ], "url": "/library-v2/LIB2-188/", "content_sha256": "d13c8c543c29af8291571463b64b83525c22e1f4c82d9b0f78f57e9475f004eb", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-189", "entry_version": 8, "class": "CLAIM", "title": "The anisotropic heat-kernel family has nonlinear OS positivity in its cone", "statement": "In the declared anisotropic heat-kernel family with α > |β|, the positive elliptic invariant generates a positive Markov convolution whose reflected-kernel factorization gives OS positivity.", "scope": { "carrier": "The anisotropic heat-kernel family generated by Lα,β", "domain": "Nonlinear reflection positivity in the declared heat-kernel family at regulator tier.", "group": null, "hypotheses": [ "Use the registered invariant operator Lα,β and its coefficient cone α > |β|.", "Use the reflected-kernel factorization of Proposition 8.5." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 307 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix T", "section": "§8, Proposition 8.5: nonlinear reflection positivity", "pdf_page": 324, "quote": "Lα,β is a positive elliptic invariant on the whole cone α > |β|, the heat semigroup is a positive Markov convolution, and the reflected-kernel factorization gives OS positivity." }, "caution": "This family-specific reflection positivity does not establish a general gravitational measure or a continuum Einstein limit.", "candidate_ids": [ "C2-094" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-170" }, { "type": "related_to", "target": "LIB2-172" } ], "url": "/library-v2/LIB2-189/", "content_sha256": "f968f54fc4ff5d174e5127863e36a508991ef0abb0b91972aa76b48d82237996", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-190", "entry_version": 8, "class": "CLAIM", "title": "No positive path in the declared heat-kernel family reaches pure MM/EH", "statement": "No continuous positive path in the declared anisotropic heat-kernel family reaches the nonzero pure MacDowell–Mansouri/Einstein–Hilbert weight.", "scope": { "carrier": "The positive anisotropic heat-kernel family and the pure MM/EH target", "domain": "The declared positive-path obstruction, not every constrained gravity construction.", "group": null, "hypotheses": [ "Restrict the path to the coefficient family and positive cone in Proposition 8.5." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 307 }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix T", "section": "§8, Proposition 8.5: positive-path obstruction", "pdf_page": 324, "quote": "But for β ̸= 0, α = 0 lies outside even the closed cone (the apex (0, 0) is in its closure; the no-path result concerns the nonzero pure-MM weight — Rev32.9, A1677 F03): no continuous positive path in this family reaches pure MM/EH." }, "caution": "This excludes only the stated path in this family, not a nonlinear simplicity-constrained completion.", "candidate_ids": [ "C2-095" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-171" }, { "type": "related_to", "target": "LIB2-172" }, { "type": "related_to", "target": "LIB2-189" } ], "url": "/library-v2/LIB2-190/", "content_sha256": "64740ec33ff23a3842bfdcfb3497bed828754dd6c752c33425a1972b80e4c941", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-191", "entry_version": 8, "class": "CLAIM", "title": "The stated bivector simplicity condition cannot be imposed by a linear projector", "statement": "Some sums of simple bivectors are nonsimple (e1∧e2 + e3∧e4 has rank 4), so no linear projector retracts onto the full simple-bivector variety; keeping the full condition needs a nonlinear construction.", "scope": { "carrier": "The bivector simplicity condition in the finite Cartan regulator", "domain": "The linear-projector route to simplicity, not the nonlinear measure that follows.", "group": null, "hypotheses": [ "Use the simple-bivector condition and sum considered in Theorem 8.6." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 307 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix T", "section": "§8, Theorem 8.6: linear-projector obstruction", "pdf_page": 324, "quote": "Some sums of simple bivectors are nonsimple (e1 ∧ e2 + e3 ∧ e4 has rank 4, while e1 ∧ e2 + e1 ∧ e3 is simple), so no linear projector retracts onto the full simple-bivector variety: keeping the full condition needs a nonlinear construction" }, "caution": "This obstruction does not exclude nonlinear simplicity measures or prove that such a measure has an Einstein limit.", "candidate_ids": [ "C2-094" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-190" } ], "url": "/library-v2/LIB2-191/", "content_sha256": "56a1f9dda5420b910e6e700cac9f79b61cb5065d684a4e857969c5903169dae8", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-192", "entry_version": 10, "class": "CLAIM", "title": "A soft positive simplicity weight exists at finite regulator", "statement": "At finite regulator, a positive nonlinear simplicity weight exists on the compact fixed-norm bivector domain (a sum-of-squares penalty in the five Pfaffian minors), with reflection positivity by the standard paired-multiplication argument at argument tier.", "scope": { "carrier": "The compact fixed-norm bivector domain and its soft nonlinear simplicity weight at finite regulator", "domain": "Finite-regulator weight existence, not a hard Pfaffian-variety measure and not a continuum gravitational universality result.", "group": null, "hypotheses": [ "Use the fixed-norm bivector domain, the sum-of-squares penalty in the five Pfaffian minors and the paired-multiplication reflection-positivity argument (argument tier) of Appendix T." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 307 }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix T", "section": "§8, Theorem 8.6: nonlinear simplicity measure", "pdf_page": 324, "quote": "A positive nonlinear simplicity weight exists at finite regulator: the sum-of-squares penalty exp(−λ i pi (B)2 ) in the five Pfaffian minors pi , on the fixed-norm P bivector domain (compact, so 0 < Z < ∞ for every λ ≥ 0), with reflection positivity by the standard paired-multiplication argument (argument-tier; s922 T6 notes)." }, "caution": "The weight is soft: its support is the whole fixed-norm domain, and the Pfaffian variety is reached only in the hard-constraint limit, which is not taken. Finite-regulator existence does not establish Einstein universality or the continuum renormalization-group limit.", "candidate_ids": [ "C2-094" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-170" }, { "type": "related_to", "target": "LIB2-189" }, { "type": "related_to", "target": "LIB2-191" }, { "type": "rests_on_premise", "target": "PRM-014" } ], "url": "/library-v2/LIB2-192/", "content_sha256": "a3505dc317432d3c3bede5485a56ca391da7c6119a3ade7b8ecf516601fc883e", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-193", "entry_version": 9, "class": "CLAIM", "title": "The registered Clifford construction has a one-particle bare gap", "statement": "The registered one-particle gap is MN = Λ√(ϕ^(2N) + 1/4), with χlocal² = 1/4 only inside the attachment; the interacting pole is open, LSZ is open and occupancy is open.", "scope": { "carrier": "The registered Clifford Hamiltonian and its zero-momentum MOS mass component", "domain": "The quasi-free one-particle gap, not a derived interacting mass spectrum.", "group": null, "hypotheses": [ "Use the Riesz–Clifford isometry, self-adjointness, equivariance, orientation and whitened-source premises.", "Retain the one-particle AX-MASS-LABEL attachment." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 310 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix T", "section": "§11, Proposition 11.3: one-particle attachment", "pdf_page": 328, "quote": "the MOS zero-momentum seed is the mass part of the derived Clifford Hamiltonian — a one-particle attachment, no coefficient chosen." }, "caution": "The bare gap does not derive an interacting rest mass, physical occupation or a successful exact single-χ ratio law.", "candidate_ids": [ "C2-090" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-174" }, { "type": "related_to", "target": "LIB2-106" } ], "url": "/library-v2/LIB2-193/", "content_sha256": "35b451278e015cbbe208e9a6eb6c5b53e247e6115682f4bd3ba3d24b83511d55", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-194", "entry_version": 10, "class": "CLAIM", "title": "The frozen Clifford law makes every registered carrier-map Gram isotropic", "statement": "On the frozen carrier, GT = (1/24)∥Pact T∥F² I2 for every carrier map T; the constants 5/12 and 1/24 are dimension-weighted restrictions of this one Clifford identity.", "scope": { "carrier": "The frozen Clifford active sector and the Gram assigned to a carrier map T", "domain": "The same-carrier isotropy law, not a statement about measured constants or unrelated carriers.", "group": null, "hypotheses": [ "Use the registered Cl(2,1) action on the active 24 and its zero action on the complementary 32." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 313 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix T", "section": "§14.1, Isotropy for every carrier map", "pdf_page": 331, "quote": "The immediate consequence is a single law covering every carrier map T :" }, "caution": "The identity does not identify a physical measurement or transfer a constant to a different carrier through an unconstructed map.", "candidate_ids": [ "C2-103" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-014" }, { "type": "related_to", "target": "LIB2-024" }, { "type": "cited_by_section", "target": "E-C05.2.claims-used" }, { "type": "cited_by_section", "target": "E-C05.2.derivation" }, { "type": "cited_by_section", "target": "E-C05.2.prior-art" }, { "type": "cited_by_section", "target": "E-C05.2.sources-receipt" } ], "url": "/library-v2/LIB2-194/", "content_sha256": "c0367447cb575c19fd418a518b80eb7f49063cdc3507b8f32a4be5dc7a81d304", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-195", "entry_version": 11, "class": "CLAIM", "title": "The frozen symplectic braid representation has a nonscalar centre", "statement": "The registered B1 and B2 give a symplectic representation B3 → Sp(V56) with nonscalar centre (B1B2)³ = I − 2Pact; only the active sector projectivizes to PSL(2,Z).", "scope": { "carrier": "The registered braid generators on the frozen real V56 carrier", "domain": "The frozen symplectic braid representation, not the winding-category functor.", "group": null, "hypotheses": [ "Use the registered B1, B2 and active-sector projector in Appendix T §14.2." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 313 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix T", "section": "§14.2, Braid representation and centre", "pdf_page": 331, "quote": "exactly and are symplectic: a genuine representation B3 → Sp(V56 ). The centre is computed and is not scalar — (B1 B2 )3 = I − 2Pact — so there is no global PSL(2, Z); only the active sector projectivizes." }, "caution": "The representation does not supply the missing functor to the winding category or identify the trace-three word with a physical lepton neck.", "candidate_ids": [ "C2-104" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-015" }, { "type": "related_to", "target": "LIB2-194" }, { "type": "related_to", "target": "LIB2-143" }, { "type": "cited_by_section", "target": "E-C05.2.claims-used" }, { "type": "cited_by_section", "target": "E-C05.2.derivation" }, { "type": "cited_by_section", "target": "E-C05.2.prior-art" }, { "type": "cited_by_section", "target": "E-C05.2.sources-receipt" } ], "url": "/library-v2/LIB2-195/", "content_sha256": "70fa18092207fb1df5172f088b93538fe3d78c8f138e23f59921ec3a7a57ac92", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-196", "entry_version": 7, "class": "CLAIM", "title": "The specified classical vacuum spectrum is reproduced by CSS charge sums", "statement": "Conditional on the κphys candidate mechanism, the specified CDIZ xi = 1 golden point reproduces all 8 gravitini, 28 vectors, 56 fermions including goldstini and 70 scalars as CSS charge sums of four gravitino masses.", "scope": { "carrier": "The classical spectrum at the specified golden point on the CDIZ locus", "domain": "The source's internal classical spectrum closure at the specified point, not a scored physical spectrum.", "group": null, "hypotheses": [ "Use xi = 1 and the stated STU data e = (0.99471,0.96943,0.94410).", "Retain Appendix Q's conditional tier on the κphys mechanism, which remains a structural candidate." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 276 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix Q", "section": "§1, Proposition 1.1: complete classical spectrum", "pdf_page": 291, "quote": "All 8 gravitini, 28 vectors, 56 fermions (including the goldstini), and 70 scalars of the N = 8 classical spectrum at the golden point are reproduced at machine precision as CSS charge sums of the four gravitino masses on the CDIZ xi = 1 locus." }, "caution": "The conditional classical-spectrum closure is not quantum stability, a Standard-Model mass spectrum or an independently verified world-facing prediction.", "candidate_ids": [ "C2-042" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-079" }, { "type": "related_to", "target": "LIB2-080" } ], "url": "/library-v2/LIB2-196/", "content_sha256": "c1379f5e5721d6bd7ecc9cbb5129e59dc671bf9d4e33cc48c189686b2efb4b60", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-197", "entry_version": 8, "class": "CLAIM", "title": "The positive congruence dressing stays inside the registered E7 group", "statement": "For the registered Cartan pair and E7-Grams A = exp(2SA), M = exp(2Φ) with SA,Φ ∈ p, the unique positive-definite symmetric solution of BAB = M has log B ∈ p and hence B ∈ E7(7).", "scope": { "carrier": "The positive-definite symmetric congruence dressing of two registered E7-Grams", "domain": "The stated congruence construction under its E7-Gram hypotheses.", "group": "E7(7)", "hypotheses": [ "Use p = span(S70) ⊂ Sym(56), k = [p,p] and e7 = k ⊕ p as the source's Cartan pair.", "Both A and M are E7-Grams of the stated exponential form; generic positive-definite matrices are not substituted." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": "E7(7)" }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 29 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "analytic", "availability": "shipped" }, { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Paper 1", "section": "§9, Theorem 9.1: congruence closure", "pdf_page": 30, "quote": "Then SPD ∩ E7(7) = exp(p) exactly, and for any two E7 -Grams A = exp(2SA ), M = exp(2Φ) with SA , Φ ∈ p, the unique SPD solution B of BAB = M satisfies log B ∈ p — i.e. B ∈ E7(7) identically." }, "caution": "The closure theorem does not apply to arbitrary Gram matrices or derive a physical mass or observation-map attachment.", "candidate_ids": [ "C2-035" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-006" }, { "type": "cited_by_section", "target": "E-C03.1.claims-used" }, { "type": "cited_by_section", "target": "E-C03.1.derivation" }, { "type": "cited_by_section", "target": "E-C03.1.prior-art" }, { "type": "cited_by_section", "target": "E-C03.1.sources-receipt" } ], "url": "/library-v2/LIB2-197/", "content_sha256": "111d6668d2b10e183adea93212c783f14cc037565b540ffbcb7984f7dcad8c22", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-198", "entry_version": 11, "class": "CLAIM", "title": "The MRSS Higgs parity is unique only under the loaded scalar spectrum", "statement": "The MRSS Higgs parity is unique conditional on the loaded low-energy scalar spectrum of one weak doublet and no coloured triplet; it is a consistency statement, not a derivation of that spectrum.", "scope": { "carrier": "The mouth-Real matrix-twist orbifold and its Higgs parity", "domain": "The conditional parity assignment, not a parent-dynamical selection of the desired spectrum.", "group": null, "hypotheses": [ "Use the registered minimal chiral lift and the loaded low-energy scalar content.", "Retain the A1472 correction to the earlier uniqueness statement." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 77 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 4", "section": "§12, A1472 correction: loaded scalar spectrum", "pdf_page": 81, "quote": "At A1472 the uniqueness was corrected: it is conditional on the loaded low-energy scalar spectrum — one weak doublet, no coloured triplet." }, "caution": "Uniqueness given the desired scalar content does not derive that content or remove its circularity risk.", "candidate_ids": [ "C2-041" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-078" }, { "type": "related_to", "target": "LIB2-098" } ], "url": "/library-v2/LIB2-198/", "content_sha256": "2ef4f2332f64fbb18943c85832e1c38c121325051bd1aafaf575ec08933766ab", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-199", "entry_version": 8, "class": "CLAIM", "title": "The weak-angle value remains a structural target on a scheme-dependent curve", "statement": "The weak-angle value ϕ⁻³ = √5 − 2 ≈ 0.23607 is retained as a roughly 2% structural target on the electroweak curve, not as a completed Z-pole prediction.", "scope": { "carrier": "The scale-free Peirce weak-angle value and its uncompleted physical matching", "domain": "The structural weak-angle target, without a completed matching-scale or threshold prescription.", "group": null, "hypotheses": [ "Retain the independent AX6 polarization postulate for the orbit branch.", "The matching scale and scheme are not derived." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "Structural", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 73 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 4", "section": "§7, Structural rather than completed precision target", "pdf_page": 77, "quote": "We therefore carry ϕ−3 as a ∼ 2% structural tree-level target on the electroweak curve, not as a completed Z-pole precision prediction." }, "caution": "The target does not select a matching scale or supply a scheme-matched electroweak precision prediction.", "candidate_ids": [ "C2-014" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-200" } ], "url": "/library-v2/LIB2-199/", "content_sha256": "5a6cc8b14f4ef873f496bdca0d79476e3175d68c09cc67caa3d1d00e3fcb6b3c", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-200", "entry_version": 12, "class": "CLAIM", "title": "The AX6 polarization postulate gives its readout without selecting itself", "statement": "AX6pol independently postulates Λ* = 3P/Q(Y) = 6ϕ − 1; its registered readout 3/(4 + Λ*) = ϕ⁻³ is an identity once that postulate is assumed.", "scope": { "carrier": "The exact-colour orbit polarization postulate and its registered weak-angle readout", "domain": "The independent polarization premise and conditional readout, not a derivation of the premise.", "group": null, "hypotheses": [ "Adopt AX6pol on the exact-colour I4 = ϕ3 orbit.", "Do not substitute the distinct retired Det2 selector or its degree argument." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 73 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 4", "section": "§7, AX6 polarization postulate", "pdf_page": 77, "quote": "AX6pol is the polarisation postulate Λ⋆ = 3P/Q(Y ) = 6ϕ − 1 on the exact-colour I4 = ϕ3 orbit" }, "caution": "The readout identity does not derive AX6pol or the low-energy matching scale, and the retired Det2 argument does not select it.", "candidate_ids": [ "C2-125" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-199" }, { "type": "rests_on_premise", "target": "PRM-006" } ], "url": "/library-v2/LIB2-200/", "content_sha256": "26e63b669b9c912a8bd9e82aac927e1beb6db6c087719d5f79bb8ac2d6e1fff5", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-201", "entry_version": 13, "class": "CLAIM", "title": "The parked moment model records a traversal with sixty winding ticks", "statement": "The parked moment model identifies one moment with a traversal of the S1/Z2 base circle, with the 56 substrate states carrying Σ|winding| = 60 ν-ticks; the interpretation remains suggestive and unpromoted.", "scope": { "carrier": "The base-circle traversal and winding count in the parked moment-ledger model", "domain": "The explicitly unpromoted moment model, outside the suite's falsifiable core.", "group": null, "hypotheses": [ "Use the parked S103 moment-ledger model, not an observed duration or an added time calibration." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 122 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 8", "section": "§4, Moment-ledger model and parking decision", "pdf_page": 126, "quote": "The S103 “moment ledger” (filed 2026-06-13, status candidate, never star-gated) is parked here by PI decision rather than promoted." }, "caution": "The parked winding count does not predict an observed duration in seconds or promote the moment interpretation to a physical result.", "candidate_ids": [ "C2-167" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-202" }, { "type": "related_to", "target": "LIB2-054" } ], "url": "/library-v2/LIB2-201/", "content_sha256": "6469d3db273a42ae96d3da2ce510a48d69b73050a5eeedf769204fb41e490dd4", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-202", "entry_version": 7, "class": "CLAIM", "title": "The specified constant set cannot supply a duration in seconds", "statement": "No monomial in the banked constants {q0clk,κ,Γ} carries a time dimension, so that mass/length-complete constant set cannot determine a duration in seconds.", "scope": { "carrier": "The banked clock, kappa and Gamma constants in the moment-ledger dimensional analysis", "domain": "The time-dimension obstruction of that specified constant set, not all augmented models.", "group": null, "hypotheses": [ "Restrict to monomials in the constant set {q0clk,κ,Γ} named by the source." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 122 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 8", "section": "§4, Time-silence dimensional obstruction", "pdf_page": 126, "quote": "no monomial in the banked constants {q0clk , κ, Γ} carries a time dimension, so a duration in seconds is not derivable from the framework’s mass/length-complete constant set" }, "caution": "The restricted dimensional obstruction does not exclude adding an external time axis or establish a measured clock period.", "candidate_ids": [ "C2-167" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-201" }, { "type": "related_to", "target": "LIB2-203" } ], "url": "/library-v2/LIB2-202/", "content_sha256": "d5fb97b8807e920f45162c18e4ed8401c7457ef2cdbfae8239cba3edf11a5632", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-203", "entry_version": 10, "class": "CLAIM", "title": "The parked Gogberashvili splice imports an external time axis", "statement": "The parked Gogberashvili splice is recorded as reconciling the house constants with an external {c,ℏ} time axis on the shared SO(4,4) signature; it remains suggestive and unpromoted.", "scope": { "carrier": "The house constants and external time axis in the parked splice", "domain": "The source's parked reconciliation, not a derived intrinsic time scale.", "group": null, "hypotheses": [ "Import the external {c,ℏ} time axis and use the shared signature named in the source." ], "physical_target": null, "quantifier": "The registered construction and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 122 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 8", "section": "§4, External time-axis splice", "pdf_page": 126, "quote": "(iii) the Gogberashvili splice reconciling the house constants with an external {c, ℏ} time axis on the shared SO(4, 4) signature." }, "caution": "The splice does not derive its external time-axis inputs or resolve time calibration from the banked constant set alone.", "candidate_ids": [ "C2-167" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-201" }, { "type": "related_to", "target": "LIB2-202" } ], "url": "/library-v2/LIB2-203/", "content_sha256": "05bcd53276e3da0a4d8f7118977172bf455d10e6605a75a3c84f8d52b96199a3", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-204", "entry_version": 8, "class": "COMPARATOR", "title": "SL-01: NuFIT solar mass-squared splitting comparator", "statement": "The ledger’s NuFIT solar mass-squared splitting comparator is 7.537e-5 eV², with asymmetric uncertainties and one shared row for fits with or without SK atmospheric data.", "scope": { "carrier": null, "domain": "NuFIT 6.1 IC24 normal ordering; with/without SK atmospheric data", "group": null, "hypotheses": [], "physical_target": "Δm²₂₁", "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 80 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "COMPARATOR", "evidence_status": [ { "kind": "external", "availability": "shipped" } ], "primary_source": { "component": "Paper 5", "section": "§2, Named splitting data beside the literal mass-reading test", "pdf_page": 84, "quote": "NuFIT 6.1 IC24 NO: ∆m221 = 7.537 × 10−5 eV2" }, "caution": null, "candidate_ids": [ "C2-179" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-204/", "content_sha256": "c75a7dedebe17696d0693546e033fcf92d95db78db7fd1ebd7063b0a6386be8e", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-205", "entry_version": 7, "class": "COMPARATOR", "title": "SL-02: NuFIT atmospheric splitting with SK-ATM", "statement": "The ledger’s normal-ordering NuFIT atmospheric mass-squared splitting comparator with SK-ATM is 2.511e-3 eV², with asymmetric uncertainties.", "scope": { "carrier": null, "domain": "NuFIT 6.1 IC24 normal ordering, with SK-ATM", "group": null, "hypotheses": [], "physical_target": "Δm²₃₁", "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 80 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "COMPARATOR", "evidence_status": [ { "kind": "external", "availability": "shipped" } ], "primary_source": { "component": "Paper 5", "section": "§2, Named atmospheric splitting beside the literal mass-reading test", "pdf_page": 84, "quote": "∆m23ℓ = 2.511 × 10−3 eV2" }, "caution": null, "candidate_ids": [ "C2-180" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-205/", "content_sha256": "868697d529e06b0bea9288896997bc7fd0849a8f4a00fb2c490611184e127edd", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-206", "entry_version": 7, "class": "COMPARATOR", "title": "SL-03: NuFIT atmospheric splitting without SK-ATM", "statement": "The ledger records the normal-ordering NuFIT atmospheric mass-squared splitting without SK-ATM, with asymmetric uncertainties.", "scope": { "carrier": null, "domain": "NuFIT 6.1 normal ordering, without SK-ATM", "group": null, "hypotheses": [], "physical_target": "Δm²₃₁", "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "COMPARATOR", "evidence_status": [ { "kind": "external", "availability": "shipped" } ], "primary_source": null, "caution": null, "candidate_ids": [ "C2-181" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-206/", "content_sha256": "4ed0d45f47410493a8e7130cec729e48740f0bfbfeab13acce1de4e21682fde3", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-207", "entry_version": 10, "class": "COMPARATOR", "title": "SL-04: DESI baseline neutrino-mass-sum upper bound", "statement": "The DESI DR2+CMB baseline bound printed in the suite is Σmν < 64.2 meV; the ledger records it as an upper bound under baseline ΛCDM, not a measured central value.", "scope": { "carrier": null, "domain": "DESI DR2+CMB baseline ΛCDM; confidence level as specified by the ledger", "group": null, "hypotheses": [ "Baseline ΛCDM and the DESI DR2+CMB combination named in the source." ], "physical_target": "Σmν", "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 80 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "COMPARATOR", "evidence_status": [ { "kind": "external", "availability": "shipped" } ], "primary_source": { "component": "Paper 5", "section": "§2, Cosmology comparator in the boundary-corollary box", "pdf_page": 85, "quote": "Cosmology comparator, source-lined: DESI DR2+CMB baseline Σmν < 64.2 meV" }, "caution": null, "candidate_ids": [ "C2-182" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-207/", "content_sha256": "bbf3b458b34d75a3780a01c84de5f49fbce4bf5c2c5a64161738ee0599862932", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-208", "entry_version": 10, "class": "COMPARATOR", "title": "SL-05: DESI Feldman–Cousins neutrino-mass-sum upper bound", "statement": "The suite’s frequentist-constrained neutrino-mass-sum bound is 53 meV; the ledger records the Feldman–Cousins upper limit rather than a measured central value.", "scope": { "carrier": null, "domain": "DESI neutrino-mass-sum constraint with the ledger’s Feldman–Cousins prescription", "group": null, "hypotheses": [ "Use the Feldman–Cousins prescription and confidence level recorded in SL-05." ], "physical_target": "Σmν", "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 80 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "COMPARATOR", "evidence_status": [ { "kind": "external", "availability": "shipped" } ], "primary_source": { "component": "Paper 5", "section": "§2, Frequentist-constrained cosmology bound", "pdf_page": 85, "quote": "the 53 meV frequentist-constrained bound is model tension, not exclusion." }, "caution": null, "candidate_ids": [ "C2-183" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-208/", "content_sha256": "ce08772fe3f05d2dd3cc3ced7233894d21041a2e92b1614d89889a74a3f9ef9b", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-209", "entry_version": 7, "class": "COMPARATOR", "title": "SL-06: MS-bar weak-angle comparator at the Z scale", "statement": "The ledger’s MS-bar weak-angle comparator at MZ is sin²θ̂W = 0.23122 ± 0.00006.", "scope": { "carrier": null, "domain": "PDG electroweak comparator in MS-bar at MZ", "group": null, "hypotheses": [], "physical_target": "sin²θ̂W(MZ)", "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 72 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "COMPARATOR", "evidence_status": [ { "kind": "external", "availability": "shipped" } ], "primary_source": { "component": "Paper 4", "section": "§7, Three distinct electroweak scheme objects", "pdf_page": 76, "quote": "sin2 θ̂W (MS, MZ ) = 0.23122 ± 0.00006" }, "caution": null, "candidate_ids": [ "C2-184" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-209/", "content_sha256": "0e98f0fdda2010b040419d6a00f783c9fcaf7dca62fc26d3dc7f24a838227324", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-210", "entry_version": 7, "class": "COMPARATOR", "title": "SL-07: MS-bar strange Yukawa comparator", "statement": "The ledger records the strange-quark Yukawa coupling in the MS-bar scheme at its stated teraelectronvolt scale, with asymmetric uncertainties.", "scope": { "carrier": null, "domain": "Source-ledger strange Yukawa comparator, MS-bar at 1 TeV", "group": null, "hypotheses": [], "physical_target": "ys", "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "COMPARATOR", "evidence_status": [ { "kind": "external", "availability": "shipped" } ], "primary_source": null, "caution": null, "candidate_ids": [ "C2-185" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-210/", "content_sha256": "c9801f9e23bbf414eaa7f05f2d1015ce669766fd50b4b6acb9a389346413a511", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-211", "entry_version": 7, "class": "COMPARATOR", "title": "SL-08: MS-bar bottom Yukawa comparator", "statement": "The ledger records the bottom-quark Yukawa coupling in the MS-bar scheme at its stated teraelectronvolt scale, with asymmetric uncertainties.", "scope": { "carrier": null, "domain": "Source-ledger bottom Yukawa comparator, MS-bar at 1 TeV", "group": null, "hypotheses": [], "physical_target": "yb", "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "COMPARATOR", "evidence_status": [ { "kind": "external", "availability": "shipped" } ], "primary_source": null, "caution": null, "candidate_ids": [ "C2-186" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-211/", "content_sha256": "b64f43d21bc1e1d75c9fcfaa62d9874bdeff2ef30d81c46cd0237089a0325111", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-212", "entry_version": 7, "class": "COMPARATOR", "title": "SL-09: Global-fit CKM Dirac phase in radians", "statement": "The ledger’s global-fit CKM Dirac-phase comparator is δ = 1.154 ± 0.025 rad.", "scope": { "carrier": null, "domain": "PDG global-fit CKM Dirac phase, radian representation", "group": null, "hypotheses": [], "physical_target": "δCKM", "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 48 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "COMPARATOR", "evidence_status": [ { "kind": "external", "availability": "shipped" } ], "primary_source": { "component": "Paper 3", "section": "§2.1, Comparator refresh: global-fit Dirac phase", "pdf_page": 50, "quote": "the global-fit Dirac phase δ = 1.154 ± 0.025 rad" }, "caution": null, "candidate_ids": [ "C2-187" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-212/", "content_sha256": "1c3fd037446c6d9c578e5e277d5a2b445b6b8027ffed54a6a3d07d042001cc80", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-213", "entry_version": 7, "class": "COMPARATOR", "title": "SL-10: Global-fit Jarlskog invariant comparator", "statement": "The ledger’s global-fit Jarlskog comparator is J = 3.16e-5, with asymmetric errors +0.13e-5 and −0.11e-5.", "scope": { "carrier": null, "domain": "PDG global-fit Jarlskog invariant", "group": null, "hypotheses": [], "physical_target": "JCKM", "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 51 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "COMPARATOR", "evidence_status": [ { "kind": "external", "availability": "shipped" } ], "primary_source": { "component": "Paper 3", "section": "Candidate Construction 2.1, Experimental Jarlskog comparator", "pdf_page": 54, "quote": "PDG 2026: J = 3.16+0.13 −5 −0.11 × 10" }, "caution": null, "candidate_ids": [ "C2-188" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-213/", "content_sha256": "211e2991ee2e8b6b7d4d02ffd6aaab468b075f0f453fb455c35349d93f68bcc9", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-214", "entry_version": 7, "class": "COMPARATOR", "title": "SL-11: First-row Cabibbo-magnitude comparator", "statement": "The ledger’s first-row-average comparator for |Vus| is 0.22431 ± 0.00085.", "scope": { "carrier": null, "domain": "PDG first-row average for |Vus|", "group": null, "hypotheses": [], "physical_target": "|Vus|", "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 47 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "COMPARATOR", "evidence_status": [ { "kind": "external", "availability": "shipped" } ], "primary_source": { "component": "Paper 3", "section": "§2, Named comparator for the corrected first-row readout", "pdf_page": 49, "quote": "compared with PDG 2026 0.22431 ± 0.00085" }, "caution": null, "candidate_ids": [ "C2-189" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-214/", "content_sha256": "16f762245466a45921ebffa7a415cab5761276f62931576593dbb9cb2cbc21ba", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-215", "entry_version": 7, "class": "COMPARATOR", "title": "SL-12: Retained PDG |Vub| comparator", "statement": "The ledger’s retained comparator for |Vub| is 0.00389 ± 0.00016.", "scope": { "carrier": null, "domain": "Retained PDG |Vub| comparator; ledger scheme wording and suite direct-value wording are both preserved", "group": null, "hypotheses": [], "physical_target": "|Vub|", "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 46 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "COMPARATOR", "evidence_status": [ { "kind": "external", "availability": "shipped" } ], "primary_source": { "component": "Paper 3", "section": "§2, Named Vub comparator", "pdf_page": 48, "quote": "Against the PDG 2026 direct value |Vub | = 0.00389 ± 0.00016" }, "caution": null, "candidate_ids": [ "C2-190" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-215/", "content_sha256": "ae5ed6f140cd0d5d3df24aa93d5bc082319724d28d3544aa6724fcdab11c159f", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-216", "entry_version": 7, "class": "COMPARATOR", "title": "SL-13: Retained PDG |Vcb| comparator", "statement": "The ledger’s retained comparator for |Vcb| is 0.0407 ± 0.0013.", "scope": { "carrier": null, "domain": "PDG global-fit |Vcb| comparator as ledgered", "group": null, "hypotheses": [], "physical_target": "|Vcb|", "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 48 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "COMPARATOR", "evidence_status": [ { "kind": "external", "availability": "shipped" } ], "primary_source": { "component": "Paper 3", "section": "§2.1, Comparator refresh: Vcb", "pdf_page": 50, "quote": "The named CKM comparators move: |Vcb | 0.0408 ± 0.0014 → 0.0407 ± 0.0013" }, "caution": null, "candidate_ids": [ "C2-191" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-216/", "content_sha256": "8f49e2be32c5d31865926baed7a153ff14e0c519a41781e13bf98c5b24b4e828", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-217", "entry_version": 7, "class": "COMPARATOR", "title": "SL-14: First-row |Vud| comparator", "statement": "The ledger’s first-row comparator for |Vud| is 0.97367 ± 0.00032.", "scope": { "carrier": null, "domain": "PDG first-row |Vud| comparator", "group": null, "hypotheses": [], "physical_target": "|Vud|", "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 46 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "COMPARATOR", "evidence_status": [ { "kind": "external", "availability": "shipped" } ], "primary_source": { "component": "Paper 3", "section": "§2, Vud comparator supplied in the suite", "pdf_page": 49, "quote": "PDG 2026 |Vud | = 0.97367 ± 0.00032" }, "caution": null, "candidate_ids": [ "C2-192" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-217/", "content_sha256": "b14a0b81369fbc568b0324ca6fe954179f986f700051a255acee32cfd882ea40", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-218", "entry_version": 7, "class": "COMPARATOR", "title": "SL-15: MS-bar charm mass at its self-scale", "statement": "The ledger’s MS-bar charm-mass comparator at the charm self-scale is mc(mc) = 1272.9 ± 4.5 MeV.", "scope": { "carrier": null, "domain": "PDG charm running mass in MS-bar at mc", "group": null, "hypotheses": [], "physical_target": "mc(mc)", "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 37 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "COMPARATOR", "evidence_status": [ { "kind": "external", "availability": "shipped" } ], "primary_source": { "component": "Paper 2", "section": "§3.6, Charm MS-bar comparator and cross-scheme boundary", "pdf_page": 38, "quote": "2026 MS comparator mc (mc ) = 1272.9 ± 4.5 MeV." }, "caution": null, "candidate_ids": [ "C2-193" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-218/", "content_sha256": "4aefec307e8e96a7bb42872bd9a7ed2f64b62ca7ea9642ae6efec2d8192b6df2", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-219", "entry_version": 7, "class": "COMPARATOR", "title": "SL-16: MS-bar bottom mass at its self-scale", "statement": "The ledger’s MS-bar bottom-mass comparator at the bottom self-scale is mb(mb) = 4186 ± 6 MeV.", "scope": { "carrier": null, "domain": "PDG bottom running mass in MS-bar at mb", "group": null, "hypotheses": [], "physical_target": "mb(mb)", "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 37 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "COMPARATOR", "evidence_status": [ { "kind": "external", "availability": "shipped" } ], "primary_source": { "component": "Paper 2", "section": "§3.6, Bottom MS-bar comparator and cross-scheme boundary", "pdf_page": 38, "quote": "against PDG 2026 mb (mb ) = 4186 ± 6 MeV" }, "caution": null, "candidate_ids": [ "C2-194" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-219/", "content_sha256": "d3bc0a2e88cdad06336ffb745a6f5190d74a46962b5a7efbfd9b257112f34344", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-220", "entry_version": 8, "class": "COMPARATOR", "title": "SL-17: Direct/MC top-mass comparator", "statement": "The ledger’s direct/MC top-mass comparator is 172.60 ± 0.27 GeV, distinct from the cross-section pole mass and not an MS-bar mass.", "scope": { "carrier": null, "domain": "PDG direct-measurement (MC) top mass; the cross-section pole mass is a distinct object", "group": null, "hypotheses": [], "physical_target": "Top direct/MC mass", "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 325 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "COMPARATOR", "evidence_status": [ { "kind": "external", "availability": "shipped" } ], "primary_source": { "component": "Appendix X", "section": "Honest precision summary, top-quark comparator", "pdf_page": 345, "quote": "PDG 2026 direct-measurement (MC) mass 172.60 ± 0.27 GeV (the cross-section pole mass is a distinct object)" }, "caution": null, "candidate_ids": [ "C2-195" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-220/", "content_sha256": "633449e91a4df71c71951b7120831f01151310603120e8af7f6460f9bfb5b0f8", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-221", "entry_version": 7, "class": "COMPARATOR", "title": "SL-18: Measured tau-mass anchor", "statement": "The ledger’s measured tau-mass anchor is mτ = 1776.93 ± 0.09 MeV.", "scope": { "carrier": null, "domain": "PDG tau pole mass used as the suite’s external charged-lepton anchor", "group": null, "hypotheses": [], "physical_target": "mτ", "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": "Input", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 333 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "COMPARATOR", "evidence_status": [ { "kind": "external", "availability": "shipped" } ], "primary_source": { "component": "Paper 2", "section": "§3.2, Equation (16): external tau anchor", "pdf_page": 34, "quote": "With the single external anchor mτ = 1776.93(9) MeV," }, "caution": null, "candidate_ids": [ "C2-196" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-221/", "content_sha256": "c501c0120278ad00bd79ed689324096f5a3fd96d5922afaad1c0c251a72b1f4e", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-222", "entry_version": 7, "class": "COMPARATOR", "title": "SL-19: Global-fit CKM Dirac phase in degrees", "statement": "The ledger’s degree presentation of the global-fit CKM Dirac phase is δ = 66.12° ± 1.43°.", "scope": { "carrier": null, "domain": "PDG global-fit CKM Dirac phase, degree representation", "group": null, "hypotheses": [], "physical_target": "δCKM", "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 48 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "COMPARATOR", "evidence_status": [ { "kind": "external", "availability": "shipped" } ], "primary_source": { "component": "Paper 3", "section": "§2.1, Comparator refresh: two presentations of the global-fit phase", "pdf_page": 50, "quote": "the global-fit Dirac phase δ = 1.154 ± 0.025 rad gives +1.40σ in that published representation, which is primary (R-29; the degree cells 66.12◦ ± 1.43◦ give +1.41σ)" }, "caution": null, "candidate_ids": [ "C2-197" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-222/", "content_sha256": "0ea35597e0d720b0b4eb34c385cf8b02e3f7f432871ffc8b90a9bea9463a5dd0", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-223", "entry_version": 7, "class": "COMPARATOR", "title": "SL-20: Direct unitarity-triangle angle comparator", "statement": "The ledger’s direct unitarity-triangle angle comparator is γ = 66.4° with asymmetric errors +2.7° and −2.8°.", "scope": { "carrier": null, "domain": "PDG direct unitarity-triangle angle measurement, not the global-fit Dirac phase", "group": null, "hypotheses": [], "physical_target": "γ", "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 48 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "COMPARATOR", "evidence_status": [ { "kind": "external", "availability": "shipped" } ], "primary_source": { "component": "Paper 3", "section": "§2.1, Comparator refresh: direct UT angle", "pdf_page": 50, "quote": "the direct UT-angle γ = 66.4+2.7 −2.8" }, "caution": null, "candidate_ids": [ "C2-198" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-223/", "content_sha256": "36aaa4f67ecbf8019920ef6afc3f7830098a8e58e10901a06e29351d5cf3a9e3", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-224", "entry_version": 7, "class": "COMPARATOR", "title": "SL-21: On-shell weak-angle comparator", "statement": "The ledger’s on-shell weak-angle comparator is 0.22348 ± 0.00010.", "scope": { "carrier": null, "domain": "PDG on-shell weak angle defined by the W/Z mass-ratio convention", "group": null, "hypotheses": [], "physical_target": "sin²θW, on-shell", "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 72 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "COMPARATOR", "evidence_status": [ { "kind": "external", "availability": "shipped" } ], "primary_source": { "component": "Paper 4", "section": "§7, Three distinct electroweak scheme objects: on-shell value", "pdf_page": 76, "quote": "the on-shell value is 0.22348 ± 0.00010" }, "caution": null, "candidate_ids": [ "C2-199" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-224/", "content_sha256": "b694bf48cc012a00167282364751e622d6776e37946b338ac825d2655b28d093", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-225", "entry_version": 7, "class": "COMPARATOR", "title": "SL-22: Effective-leptonic weak-angle comparator", "statement": "The ledger’s effective-leptonic weak-angle comparator is 0.23161 ± 0.00004.", "scope": { "carrier": null, "domain": "PDG effective leptonic weak angle", "group": null, "hypotheses": [], "physical_target": "sin²θeff, leptonic", "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 72 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "COMPARATOR", "evidence_status": [ { "kind": "external", "availability": "shipped" } ], "primary_source": { "component": "Paper 4", "section": "§7, Three distinct electroweak scheme objects: effective-leptonic value", "pdf_page": 76, "quote": "the effective leptonic value 0.23161 ± 0.00004 — three distinct scheme objects" }, "caution": null, "candidate_ids": [ "C2-200" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-225/", "content_sha256": "928d865580d318418fe3cfe86a79a36755ede9cde8948aaf57cbddefa5735a5a", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-226", "entry_version": 7, "class": "COMPARATOR", "title": "SL-23: NuFIT squared-sine reactor-angle comparator", "statement": "The ledger’s normal-ordering squared-sine reactor-angle comparator is 0.02248 with asymmetric errors +0.00055 and −0.00059.", "scope": { "carrier": null, "domain": "NuFIT 6.1 NH global fit (IC24); the suite specifies with SK atmospheric data", "group": null, "hypotheses": [], "physical_target": "sin²θ13", "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 79 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "COMPARATOR", "evidence_status": [ { "kind": "external", "availability": "shipped" } ], "primary_source": { "component": "Paper 5", "section": "§2, Precision and structural status: named reactor comparator", "pdf_page": 83, "quote": "comparator NuFIT 6.1 (NH, w/SK), sin2 θ13 = 0.02248+0.00055 −0.00059" }, "caution": null, "candidate_ids": [ "C2-201" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-226/", "content_sha256": "cd74e08a9adef6a21fb7a3aee5553d45e5d27b17cf4ec579378c316c1495ae5c", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-227", "entry_version": 7, "class": "COMPARATOR", "title": "SL-24: NuFIT solar angle in degrees", "statement": "The ledger’s normal-ordering solar-angle comparator is 33.76° with asymmetric errors +0.42° and −0.41°.", "scope": { "carrier": null, "domain": "NuFIT 6.1 NH global fit; the suite’s comparison table specifies IC24 NO with SK", "group": null, "hypotheses": [], "physical_target": "θ12", "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 82 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "COMPARATOR", "evidence_status": [ { "kind": "external", "availability": "shipped" } ], "primary_source": { "component": "Paper 5", "section": "§2.1, Framework versus NuFIT comparison: solar-angle comparator", "pdf_page": 86, "quote": "33.76+0.42 −0.41 ◦ (NuFIT 6.1" }, "caution": null, "candidate_ids": [ "C2-202" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-227/", "content_sha256": "80930d79f8458a31bef1296d1d6fe02c95c2901d9ba6d0fe5f6e0ea8049002f5", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-228", "entry_version": 8, "class": "COMPARATOR", "title": "SL-26: NuFIT reactor angle in degrees", "statement": "The ledger’s normal-ordering reactor-angle comparator is 8.623° with asymmetric errors +0.106° and −0.115°, the degree push-forward of the same squared-sine fit.", "scope": { "carrier": null, "domain": "NuFIT 6.1 NH reactor angle in degrees; the suite identifies the same with-SK fit as SL-23", "group": null, "hypotheses": [], "physical_target": "θ13", "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 82 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "COMPARATOR", "evidence_status": [ { "kind": "external", "availability": "shipped" } ], "primary_source": { "component": "Paper 5", "section": "§2.1, Reactor comparison box: degree push-forward", "pdf_page": 87, "quote": "In degrees, the same comparator pushes forward to θ13 = 8.623+0.106 ◦ ◦ −0.115 ," }, "caution": null, "candidate_ids": [ "C2-204" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-228/", "content_sha256": "d969a65279f1ee1e11e75db2151ac153e963945ba51e27d59d6df3e64b354b7c", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-229", "entry_version": 10, "class": "COMPARATOR", "title": "SL-27: House-computed candidate coefficient diagnostic", "statement": "The ledger’s house-computed, scheme-dependent coefficient diagnostic is 4.9635 ± 0.087; it is not a PDG measurement.", "scope": { "carrier": null, "domain": "House-computed candidate coefficient; Appendix G says the hadronic-anchor rounding convention dominates", "group": null, "hypotheses": [], "physical_target": "Candidate coefficient diagnostic", "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 189 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "COMPARATOR", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix G", "section": "§6, Fences and language, item (4): coefficient diagnostic", "pdf_page": 195, "quote": "the required coefficient is 4.9635 ± 0.087" }, "caution": null, "candidate_ids": [ "C2-205" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-229/", "content_sha256": "37c776c77d272969c531025da86a452144a41c6bf82040f015b3ba5d5ac0b3cd", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-230", "entry_version": 8, "class": "COMPARATOR", "title": "SL-28: Historical PDG |Vcb| comparator", "statement": "The historical comparator for |Vcb| was 0.0408 ± 0.0014 and is retained only as the earlier value in the printed comparator transition.", "scope": { "carrier": null, "domain": "Historical PDG 2024 global-fit |Vcb| comparator, superseded in the current comparison by SL-13", "group": null, "hypotheses": [], "physical_target": "|Vcb|, historical comparator", "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 48 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "COMPARATOR", "evidence_status": [ { "kind": "external", "availability": "shipped" } ], "primary_source": { "component": "Paper 3", "section": "§2.1, Comparator refresh: historical Vcb value", "pdf_page": 50, "quote": "The named CKM comparators move: |Vcb | 0.0408 ± 0.0014 → 0.0407 ± 0.0013" }, "caution": null, "candidate_ids": [ "C2-206" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-230/", "content_sha256": "74fcbe99b1bd8e6e9049cff50ab30a77baf3934fb95d67065c55752c9abb8e8b", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-231", "entry_version": 8, "class": "COMPARATOR", "title": "SL-29: Historical PDG |Vub| comparator", "statement": "The historical comparator for |Vub| was 0.00382 ± 0.00024 and is retained only as the earlier value in the printed comparator transition.", "scope": { "carrier": null, "domain": "Historical PDG 2024 |Vub| comparator, superseded in the current comparison by SL-12", "group": null, "hypotheses": [], "physical_target": "|Vub|, historical comparator", "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 48 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "COMPARATOR", "evidence_status": [ { "kind": "external", "availability": "shipped" } ], "primary_source": { "component": "Paper 3", "section": "§2.1, Comparator refresh: historical Vub value", "pdf_page": 50, "quote": "|Vub | 0.00382 ± 0.00024 → 0.00389 ± 0.00016" }, "caution": null, "candidate_ids": [ "C2-207" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-231/", "content_sha256": "19381173b31f517e76131fbed56e4f597c03137854b59a319f345ae77f04e620", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-232", "entry_version": 7, "class": "COMPARATOR", "title": "SL-30: Global-fit Jarlskog comparator in the printed scaled units", "statement": "The ledger’s scaled-unit presentation of the global-fit Jarlskog comparator is 3.16 with errors +0.13 and −0.11, in units of 1e-5.", "scope": { "carrier": null, "domain": "PDG global-fit Jarlskog invariant in the ledger’s printed 1e-5 units", "group": null, "hypotheses": [], "physical_target": "JCKM, scaled-unit presentation", "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 51 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "COMPARATOR", "evidence_status": [ { "kind": "external", "availability": "shipped" } ], "primary_source": { "component": "Paper 3", "section": "Candidate Construction 2.1, Experimental Jarlskog comparator", "pdf_page": 54, "quote": "PDG 2026: J = 3.16+0.13 −5 −0.11 × 10" }, "caution": null, "candidate_ids": [ "C2-208" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-232/", "content_sha256": "02caec73b5e2d4f24895fee924b2f7482a82955fbc9b05b15f0a6fdbd44c4dec", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-233", "entry_version": 7, "class": "RETIRED", "title": "Retired blanket zero-parameter observable headline", "statement": "The archived observable summary presented a blanket zero-parameter headline.", "scope": { "carrier": null, "domain": "The old programme-wide headline, not the exactness of individual algebraic formulas.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 0", "section": "Claim-language convention, S112 enforcement rule", "pdf_page": 8, "quote": "Phrasings such as “100/100,” “all green,” “zero free parameters” (for the suite as a whole), “closed,” and “emergence” are retired except where a Proved-tier theorem licenses them." }, "caution": "Retiring the blanket headline does not refute each formula or erase the explicitly loaded map's internal parameter economy.", "candidate_ids": [ "C2-098" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-233/", "content_sha256": "9fc38c0d26afe1afa45e83b4fc80979397c3ae6fd529cce878fb1fd935e4dde4", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-234", "entry_version": 7, "class": "RETIRED", "title": "Retired 20/20 Standard-Model completion headline", "statement": "The archived strange-sector proof title advertised completion of the Standard-Model observable ledger.", "scope": { "carrier": null, "domain": "The completion clause of the old strange-sector title, not every statement about the strange constituent proxy.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 0", "section": "Claim-language convention, S112 enforcement rule", "pdf_page": 8, "quote": "Phrasings such as “100/100,” “all green,” “zero free parameters” (for the suite as a whole), “closed,” and “emergence” are retired except where a Proved-tier theorem licenses them." }, "caution": "This retirement concerns the completion headline, not a claim that every archived calculation or the current strange proxy is false.", "candidate_ids": [ "C2-023" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-234/", "content_sha256": "cc754af5187547060f126bd6ef395fce06e45d0bf034ea54adbe0bf2cd0e87db", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-235", "entry_version": 9, "class": "RETIRED", "title": "Superseded three-of-eight mixing tally and pending atmospheric hold", "statement": "The earlier mixing summary retained a three-of-eight tally while the physical atmospheric-octant attachment remained on a pending hold.", "scope": { "carrier": null, "domain": "The former Track-2 mixing-summary state, not the internal atmospheric mismatch identity.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 3", "section": "§5.4, Current physical-row tally", "pdf_page": 63, "quote": "Two physical rows sit at derived-conditional, each with its premise printed beside it rather than PMNS and δ buried: θ12 CP ." }, "caution": "The retyped physical tally leaves the internal mismatch identity and its numerical value unchanged.", "candidate_ids": [ "C2-098" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-235/", "content_sha256": "13c18df7a3b1befc0af506c9942b3795d8111d693a74198cc22b85bd985dda00", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-236", "entry_version": 7, "class": "RETIRED", "title": "Retired Wyler bounded-domain derivation of alpha", "statement": "The earlier bounded-domain programme presented Wyler normalization as a derivation of the electromagnetic fine-structure constant.", "scope": { "carrier": null, "domain": "The physical alpha derivation, including its flagged reduction and domain-selection subprogramme, not pure boundary-volume identities.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" }, { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix N", "section": "§1.1, Retirement of the bounded-domain alpha derivation", "pdf_page": 264, "quote": "The bounded-domain programme is retired as a derivation of α." }, "caution": "The physical-route retirement does not declare every Wyler evaluation, class identity or boundary-volume calculation mathematically false.", "candidate_ids": [ "C2-137", "C2-153", "C2-175" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-236/", "content_sha256": "5aafd95119ed2b05e2cb414af3ff9cf0c9ef03f31785f6a08e6facac57b61352", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-237", "entry_version": 7, "class": "RETIRED", "title": "Retired exact-framework Cabibbo correction 0.225247", "statement": "The earlier hand-calculated correction presented |Vus| = 0.225247 as the exact-framework Cabibbo readout.", "scope": { "carrier": null, "domain": "The incorrect canonical decimal, distinct from the framework formula and measured-angle diagnostic.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 3", "section": "§2, Hand-calculated correction withdrawn", "pdf_page": 49, "quote": "the Rev32.5 “correction” to 0.225247/33.4877◦ was itself a hand calculation that matched no angle in the chain — the digit we got wrong twice, corrected Rev32.6 from s1162, A1572)" }, "caution": "Correcting the decimal does not derive the loaded route choice or change the separate exact block weight.", "candidate_ids": [ "C2-009", "C2-062" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-237/", "content_sha256": "fadc572fe172f9d922e0ab377b9ec6811efdb09eec59dc26bf02754a22a641af", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-238", "entry_version": 7, "class": "RETIRED", "title": "Superseded rounded-angle Cabibbo value as the canonical readout", "statement": "The earlier canonical Cabibbo display used 0.225268, obtained from the rounded solar angle 33.49°.", "scope": { "carrier": null, "domain": "The former canonical use of a rounded-angle evaluation, not a claim that evaluating that rounded angle is invalid.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 3", "section": "§2, Rounded-angle value and its former use", "pdf_page": 49, "quote": "the rounded display angle 33.49◦ gives 0.225268, the figure printed through Rev32.4;" }, "caution": "The rounded-input evaluation remains a distinct diagnostic; only its use as the canonical exact-framework value is superseded.", "candidate_ids": [ "C2-009" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-238/", "content_sha256": "b2de3b682fa3aaedbe9334237fdcfba94bcdb1ba96c72c5fc930cfd7c384e674", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-239", "entry_version": 10, "class": "RETIRED", "title": "Deprecated house Cabibbo-comparator route", "statement": "The earlier house Cabibbo note presented CF2 Route B as its primary, GREEN route; a header added later marks the note deprecated, quoting a suite sentence that deprecates the Cabibbo-comparator route and keeps Route B canonical.", "scope": { "carrier": null, "domain": "The particular house Cabibbo route identified by its supplied header and S270 flag.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 3", "section": "§2, Route-selection provenance", "pdf_page": 49, "quote": "The first row is Loaded: Route B was selected after comparison with kaon data." }, "caution": "This retirement does not retire the current loaded Route-B formula merely because both descriptions use the Route-B name.", "candidate_ids": [ "C2-147" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-239/", "content_sha256": "1459148292705523444acc924cdfa484366cd3b8cde0b7d097799d4e8c3c5558", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-240", "entry_version": 7, "class": "RETIRED", "title": "Retired Shilov atmospheric-angle derivation", "statement": "The earlier atmospheric-angle route presented a Shilov-boundary correction as the operative prediction.", "scope": { "carrier": null, "domain": "The earlier Shilov atmospheric readout, distinct from the separate rational atmospheric assertion.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 7", "section": "§7, Atmospheric-angle precedent", "pdf_page": 120, "quote": "The current framework value is the mismatch-geometry branch sin2 θ23 = 7/16, rather than the older higher-octant phenomenological placeholder — printed since Rev32.6 as the sharp loaded lower-branch target of the selected corre- spondence (A1566: the octant registration is a candidate map, not a selector; the internal identity stays theorem-grade)." }, "caution": "The old arctangent target is not the separate retired rational target, and the new physical branch remains a loaded correspondence.", "candidate_ids": [ "C2-168" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-240/", "content_sha256": "760b61006b1cb95b8e3c80ab36fade0b4aa821f2ea8391a4517f60e155b7d764", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-241", "entry_version": 8, "class": "RETIRED", "title": "Retired claim that the chirality interface selected the atmospheric octant", "statement": "The earlier atmospheric account claimed that the chirality interface had built the octant selector and locked the branch, thereby reducing the free-bit count.", "scope": { "carrier": null, "domain": "The withdrawn physical selection and bit-reduction interpretation of the chirality interface.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix N", "section": "§6, Retired octant-selection assertions", "pdf_page": 269, "quote": "The Rev32.5 claims “selector built”, “locked to εQ ” and “free bits 2 → 1” are retired." }, "caution": "The retirement leaves the internal mismatch identity intact and does not select the opposite physical octant.", "candidate_ids": [ "C2-005", "C2-059" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-241/", "content_sha256": "ef93ff3f5eef5fb20b0b668e337d27f2dab25d906694f0992a49221dc80ffa63", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-242", "entry_version": 9, "class": "RETIRED", "title": "Superseded trimaximal cosine-phase correction apparatus", "statement": "The house carried an erratum to a reported cos δ_TM1 value within the trimaximal (TM1) mixing apparatus; a header added later flags that apparatus as retired; the current print types δCP = −2π/√5 = −160.997° Derived-conditional (Rev29 re-tiering; the pre-Rev29 stamp was Theorem ⋆100).", "scope": { "carrier": null, "domain": "The former use of the named cosine-phase erratum in the trimaximal apparatus, not a finding that the correction's algebra is false.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 5", "section": "§3, Retained leptonic-phase readout", "pdf_page": 88, "quote": "δCP = −2π/ 5 = −160.997◦" }, "caution": "Supersession of the apparatus does not show that the historical erratum was mathematically incorrect.", "candidate_ids": [ "C2-152" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-242/", "content_sha256": "3551423bab7a7c0db2cabdb13529d5de304e40c7281a264aa080be5f8ee92099", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-243", "entry_version": 8, "class": "RETIRED", "title": "Superseded trimaximal condition and rho-modulus apparatus", "statement": "The house once carried a trimaximal condition and rho modulus requiring an extra postulate as part of its mixing apparatus; the current print types δCP = −2π/√5 = −160.997° Derived-conditional (Rev29 re-tiering; the pre-Rev29 stamp was Theorem ⋆100).", "scope": { "carrier": null, "domain": "The former operative trimaximal condition and its independent-postulate role.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 5", "section": "§3, Retained leptonic-phase readout", "pdf_page": 88, "quote": "δCP = −2π/ 5 = −160.997◦" }, "caution": "Retiring this apparatus does not refute its stated postulate independence or derive all current mixing attachments.", "candidate_ids": [ "C2-173" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-243/", "content_sha256": "52039039cf202a3a07b93075a83d5f0c12b1342a063fb6300bf81fa25ead4ea9", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-244", "entry_version": 9, "class": "RETIRED", "title": "Superseded hybrid leptonic-phase formula", "statement": "The earlier house hybrid-phase entry claimed a derived sign while retaining a proposed index and carried a hybrid formula as its leptonic phase target; the current print types δCP = −2π/√5 = −160.997° Derived-conditional (Rev29 re-tiering; the pre-Rev29 stamp was Theorem ⋆100).", "scope": { "carrier": null, "domain": "The physical hybrid-phase target as recorded by the supplied house header.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 5", "section": "§3, Retained leptonic-phase readout", "pdf_page": 88, "quote": "δCP = −2π/ 5 = −160.997◦" }, "caution": "The replacement readout remains conditional and does not establish equivalence between the old hybrid expression and other phase formulas.", "candidate_ids": [ "C2-159" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-244/", "content_sha256": "01131a39aa08ddcf37376abef754e5b3f722e8eb338d5a634eb7b7592dcfe8d7", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-245", "entry_version": 8, "class": "RETIRED", "title": "Retired physical use of the PSL class-algebra sign argument", "statement": "The earlier class-algebra argument used a vanishing structure constant to select the sign of a leptonic phase formula; the current print types δCP = −2π/√5 = −160.997° Derived-conditional (Rev29 re-tiering; the pre-Rev29 stamp was Theorem ⋆100), from the V3 rotation and not from that argument.", "scope": { "carrier": null, "domain": "The deprecated phase-derivation application, not the retained class-algebra coefficients.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 8", "section": "§2, Retired physical use of the class-algebra constants", "pdf_page": 122, "quote": "That application is deprecated. The authoritative CP phase is δCP = −2π/ 5 = −160.997◦ from the V3 rotation (Derived-conditional after the Rev29 re-tiering; pre-Rev29 stamp ⋆100; Paper 5, Appendix C), which does not involve PSL(2, 7) at all;" }, "caution": "The pure class-algebra constants survive, and the old phase expression remains only as a labelled cross-check.", "candidate_ids": [ "C2-172" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-057" } ], "url": "/library-v2/LIB2-245/", "content_sha256": "00120f5b500ac07f8e790412999e5274f674825a14429d467cfa8c03b2a9816b", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-246", "entry_version": 7, "class": "RETIRED", "title": "Retired legacy baryon-to-meson mass ratio", "statement": "The earlier ambient-Hessian calculation presented a baryon/meson mass ratio of approximately 6.7 as reproducing one hadron ratio.", "scope": { "carrier": null, "domain": "The old free-coupling numerical ratio in the legacy ambient-Hessian parametrization, not the retained cubic-channel argument.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 8", "section": "§4, Historical baryon/meson mass ratio", "pdf_page": 125, "quote": "A self-consistent Faddeev-pole gap equation produced a baryon/meson mass ratio MB /MM ≈ 6.7, matching the PDG proton/pion value 938/140 at a single free coupling α ≈ 0.0025 (the ratio stays in 5–8 across all perturbative α)." }, "caution": "The numerical retirement does not retire the separate tensor-structure statement that the cubic baryonic channel survives the quadratic cancellation.", "candidate_ids": [ "C2-142" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-246/", "content_sha256": "8d660755e7b3c522695fafca0c5b95dadd56944afc39ac9e81c6df191c7c385d", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-247", "entry_version": 7, "class": "RETIRED", "title": "Withdrawn proof and zero-parameter status of the muon-to-tau ratio", "statement": "The earlier charged-lepton account classified the muon-to-tau ratio as proved and carrying zero free parameters.", "scope": { "carrier": null, "domain": "The former physical derivation and parameter-status claim, not the continued use of the ratio formula.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 2", "section": "§3.2, Former proof/parameter classification withdrawn", "pdf_page": 34, "quote": "Both ingredients were previously typed Proved, and the formula was cited as carrying zero free parameters. That typing is withdrawn." }, "caution": "The typing is withdrawn while the ratio remains a structural loaded correspondence with its numerical reproduction intact.", "candidate_ids": [ "C2-018", "C2-056" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-247/", "content_sha256": "18ce8d3f3aa95c154b315a21656eced4a695aa0127cb3d9a687509e7db7f4583", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-248", "entry_version": 7, "class": "RETIRED", "title": "Withdrawn universal two-parameter mass-completion no-go", "statement": "The earlier mass-completion account claimed that every completion with at most two parameters was impossible.", "scope": { "carrier": null, "domain": "The withdrawn universal parameter-count exclusion, not the exact single-chi additive class.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix O", "section": "§5, Remark 5.2: withdrawn universal parameter bound", "pdf_page": 276, "quote": "The blanket “≤ 2-parameter completion is impossible” claim is therefore withdrawn; the honest statement is that surveyed one-parameter forms fail and no universal ≤ 2-parameter no-go is proved." }, "caution": "Withdrawing the universal claim does not rescue the exact single-chi class or make the fitted harmonic a derived replacement law.", "candidate_ids": [ "C2-055" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-248/", "content_sha256": "bc8699ed8490f1532f33d0b8c32252db3c9764939d62a0ed198bb0f7b29bce07", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-249", "entry_version": 7, "class": "RETIRED", "title": "Retired Det-squared selection of the polarization postulate", "statement": "The former weak-angle account used the Det-squared construction as the selector of the independent polarization postulate.", "scope": { "carrier": null, "domain": "The identification of the two former AX6 objects, not the mathematics of the separate Det-squared construction.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 4", "section": "§7, Two objects formerly named AX6", "pdf_page": 77, "quote": "The Det2 object is therefore retired as a selector of AX6pol ; A667 remains correct for the 50◦ object only and does not constrain AX6pol ." }, "caution": "The retirement does not refute the separate Galois argument or derive the polarization postulate and its physical matching scale.", "candidate_ids": [ "C2-125" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-249/", "content_sha256": "316de35c0972bb34d8b660b44831b01113b504000dd59f33e1aedaac9cefe639", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-250", "entry_version": 7, "class": "RETIRED", "title": "Withdrawn Schur-only proof of vanishing triplet masses", "statement": "The earlier proof sketch inferred vanishing triplet entries at every loop order from Schur block structure alone.", "scope": { "carrier": null, "domain": "The withdrawn zero-eigenvalue and all-orders inference, not the scalar-block structure or the separate numerical zero-mode result.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix A", "section": "§A.7, Schur gauge-protection withdrawal", "pdf_page": 151, "quote": "the previous version of this sketch concluded “zero entries for all triplet components at every loop order” from the block structure; that inference is withdrawn — Schur permits a nonzero scalar on each triplet block," }, "caution": "The withdrawn proof does not remove Schur block structure or independently overturn the reported numerical zeros.", "candidate_ids": [ "C2-114" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-250/", "content_sha256": "249e831e3eccfdb901a251c4ad539e8ed57f7a78cf7f6d6ba444c4929862e9a8", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-251", "entry_version": 8, "class": "RETIRED", "title": "Scoped withdrawal of blanket Artin protection for Yukawa loops", "statement": "The earlier renormalization claim treated Yukawa and gauge running as fully protected by Artin without a diagram-by-diagram internal-generator census.", "scope": { "carrier": null, "domain": "The former blanket protection claim for generic cross-block vertex corrections, not Artin protection when two-generated containment holds.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix A", "section": "§A.7.8, Generic cross-block containment gap", "pdf_page": 153, "quote": "for the generic cross-block Yukawa trilinear (three independent split-octonion entries, Paper 6) that containment is not established — momentum conservation constrains momenta, not the number of independent internal octonionic directions" }, "caution": "This scope withdrawal does not deny associativity for two-generated subalgebras or refute the separately specified lepton–photon sector.", "candidate_ids": [ "C2-114" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-251/", "content_sha256": "2369d69945c01ffe48f2ab09647a7cb1b59d717c52edbfc377cf0f0f8da8e5aa", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-252", "entry_version": 7, "class": "RETIRED", "title": "Withdrawn canonical reactor half-angle from the moment law", "statement": "Earlier wording treated the reactor half-angle as canonical solely by appeal to the symplectic moment half-turn law.", "scope": { "carrier": null, "domain": "The claimed forcing of the reactor readout rule, not the moment operator identity or the retained reactor formula.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix B", "section": "The T-bridge does not canonicalize the half-angle", "pdf_page": 160, "quote": "Earlier wording made the half-angle π/8 canonical by appeal to T 2 = −1. That inference is withdrawn." }, "caution": "The retraction leaves the moment law and the numerical reactor formula intact while withholding a derivation of its readout rule.", "candidate_ids": [ "C2-006", "C2-060" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-252/", "content_sha256": "9944e66bdcaac81052e50f9bbe16fdfa0199b5b3f16f973b411d4e04c6225385", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-253", "entry_version": 7, "class": "RETIRED", "title": "Retired structural derivation rating of the CKM phase construction", "statement": "The earlier CKM phase account gave its readout-conditioned construction a structural derivation rating despite the missing selection of its correction term.", "scope": { "carrier": null, "domain": "The former proof and structural-derivation wording, not the retained phase numeral or its comparisons.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix B", "section": "§B.6, Current phase provenance and retired wording", "pdf_page": 160, "quote": "The Dirac phase δCKM is not of that grade: it is a candidate construction under a named readout axiom (stated immediately below), i.e. a Coincidence-class numeral with an algebraic identity behind it and no selection of G7 (Rev32.5 retype; the Rev29 “Structural claim with a derivation path” wording is retired)." }, "caution": "The re-tiering does not delete the numeral, supply a correction-term selector or merge the global-fit phase with the direct UT angle.", "candidate_ids": [ "C2-012", "C2-065" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-253/", "content_sha256": "c4fd2929723b2a62decbf6d2686b7aaca8b2e0558f0db59ccba6952d70d6e6ca", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-254", "entry_version": 7, "class": "RETIRED", "title": "Withdrawn universal claim that inequality conditions cannot reduce dimension", "statement": "The earlier selector argument ruled out every positivity or stability refinement on the premise that inequality conditions cannot reduce dimension.", "scope": { "carrier": null, "domain": "The universal inequality argument, not the bounded conclusion for the banked non-degenerate stability conditions.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix E", "section": "Selection frontier F-SEL(c), withdrawal (a)", "pdf_page": 178, "quote": "The house’s universal cone claim is withdrawn. An earlier banked argument held that no positivity- or stability-type refinement could answer the question because inequality conditions cannot reduce dimension." }, "caution": "The withdrawal does not make the tested stability conditions select a ray or derive the adopted action-shape principle.", "candidate_ids": [ "C2-121" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-254/", "content_sha256": "83af17c3ffa01cc5bce0d979c52867dc9ccfde1203822968f01940ece75a84ca", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-255", "entry_version": 7, "class": "RETIRED", "title": "Retired use of one operator name for Wick chart and shell reversal", "statement": "The earlier geometry account treated the single label W as covering both the compact/split Wick chart and the shell-orientation reversal.", "scope": { "carrier": null, "domain": "The former identification hidden by the shared operator name, not either of the two correctly separated operators.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix T", "section": "§2, Theorem 2.1: two distinct operators", "pdf_page": 317, "quote": "The programme’s informal label “W ” denoted two categorically different operators." }, "caution": "Retiring the shared name does not invalidate either separated operator or identify their actions on the grading.", "candidate_ids": [ "C2-089" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-012" } ], "url": "/library-v2/LIB2-255/", "content_sha256": "78ab7f4f6fb383fa622c8f3ab3035b240860cb37f8ea2a04afa01e6fbefe1175", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-256", "entry_version": 7, "class": "RETIRED", "title": "Superseded nontrivial bundle reading of the signature sheets", "statement": "The earlier signature-sheet account described the two real-form presentations as a nontrivial bundle rather than a real-form correspondence.", "scope": { "carrier": null, "domain": "The old bundle interpretation at the ordinary real frame-preserving tier, not every reduced clutching class.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix T", "section": "§3, Named datum 3.5: corrected object", "pdf_page": 318, "quote": "a real-form correspondence, not a nontrivial bundle. The two signature presentations are two real structures in one complexified Albert fibre;" }, "caution": "This replacement does not deny the separately priced reduced clutching class or construct a physical observation map.", "candidate_ids": [ "C2-089" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-012" }, { "type": "related_to", "target": "LIB2-013" } ], "url": "/library-v2/LIB2-256/", "content_sha256": "04630a51e5ef4992dbeffd7f55062b63de10c605dbc2f4918916214107179a82", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-257", "entry_version": 7, "class": "RETIRED", "title": "Retired one-bit accounting of distinct gluing and observation structures", "statement": "The earlier accounting charged local overlap, global holonomy, real-form correspondence and physical observation as one W bit.", "scope": { "carrier": null, "domain": "The conflated accounting row, distinct from the operator-name conflation and the nontrivial-bundle interpretation.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix T", "section": "§3, Remark 3.8: distinct structures", "pdf_page": 318, "quote": "Local overlap ̸= global holonomy ̸= Real-form correspondence ̸= physical observation map." }, "caution": "Separating the accounting does not construct the observation map or determine a total physical freedom count.", "candidate_ids": [ "C2-088" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-005" } ], "url": "/library-v2/LIB2-257/", "content_sha256": "3ac42414ac4cd9789bb3704f6d9841f25d5d0e21232e37c6703596876af4aed1", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-258", "entry_version": 7, "class": "RETIRED", "title": "Retired finite-sign chamber-lift price computed on the wrong carrier", "statement": "The earlier chamber-lift row inferred a finite orthogonal-sign ambiguity from a commutant calculated on the wrong permutation carrier.", "scope": { "carrier": null, "domain": "The discrete chamber-lift price derived from the wrong carrier, not the conclusion about continuous exported freedom.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix T", "section": "§9 preamble, S253 erratum: wrong-carrier calculation", "pdf_page": 325, "quote": "The commutant-3 count was computed on the wrong carrier — the 5-point permutation module" }, "caution": "The corrected complement-frame gauge does not add continuous observable freedom or select the microscopic observation functor.", "candidate_ids": [ "C2-093" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-174" } ], "url": "/library-v2/LIB2-258/", "content_sha256": "6c3ba7b021ae4f0c3609b48bc9bc30c6bbc30abaa9b3cf68591ca37c7ab30110", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-259", "entry_version": 7, "class": "RETIRED", "title": "Withdrawn aggregate bit-and-dimension freedom headline", "statement": "The earlier freedom ledger combined a bit total, a dimension count and a surplus into one headline before computing the observation-functor faithfulness kernel.", "scope": { "carrier": null, "domain": "The former aggregate freedom count, not every individual input or surviving modulus in the typed ledger.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix X", "section": "§1.3, Typed freedom ledger replacing the headline", "pdf_page": 361, "quote": "The Rev27-era headline (a bit total plus a dimension count, with a surplus) is withdrawn pending typed rebuild: its 17-dimensional decomposition is internally inconsistent as typed — confirmed at primary source, lane-caught, and logged as a house casualty below. It is replaced by typed rows." }, "caution": "The withdrawal does not erase the separately typed data or license a replacement scalar total without a faithfulness analysis.", "candidate_ids": [ "C2-088", "C2-067" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-259/", "content_sha256": "985e6563af1bc4ecd9aa808f087011ac815fb38ce129d6c1a06186d86a8a8596", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-260", "entry_version": 8, "class": "RETIRED", "title": "Retired microscopic selector-deriving status of the earlier parent action", "statement": "The earlier microscopic-parent account claimed that its root-line minimum fixed every coefficient without an unselected marking or orientation branch.", "scope": { "carrier": null, "domain": "The selector-deriving interpretation of the D1125 action, not its consistency as a loaded finite effective action.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix S", "section": "§8.1, Consequence for the earlier parent action", "pdf_page": 308, "quote": "D1125 is killed as a selector-deriving microscopic parent action. It survives as a mathematically consistent loaded finite effective action once TAM , the copy metric and the discrete marking are declared inputs — a demotion of provenance, not an algebraic inconsistency." }, "caution": "The demotion does not make the loaded finite action algebraically inconsistent or close the physical parent-action problem.", "candidate_ids": [ "C2-105" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-021" } ], "url": "/library-v2/LIB2-260/", "content_sha256": "2ac25cac4fda57c858695d6e5c5d8c382a1b21161e61fca20cf38c4a54dd8a1f", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-261", "entry_version": 7, "class": "RETIRED", "title": "Retired independent-channel source doorway", "statement": "The earlier source model treated the two channel patterns as independent rather than as the images of one common selector contrast.", "scope": { "carrier": null, "domain": "The earlier independent-channel model in the selector arc, not a universal prohibition on independent sources in other models.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix S", "section": "§4, Paired-source replacement", "pdf_page": 304, "quote": "The correct source model (correcting the retired house doorway, casualty #4) is a single common selector contrast, not independent channel patterns." }, "caution": "The paired-source replacement does not select the common contrast or remove the separate arrow-selection problem.", "candidate_ids": [ "C2-105" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-261/", "content_sha256": "d3fe2d5466c78461c180a2a09f059c0fdad10912dcadc6b64be1cee230c5c749", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-262", "entry_version": 8, "class": "RETIRED", "title": "Withdrawn unconditional action preference for the root line", "statement": "The earlier selector account said the action voted for the root line without carrying the common-lift condition required by that preference.", "scope": { "carrier": null, "domain": "The unconditional root-line selection wording, not the common-lift-conditional extremum statement.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix S", "section": "§5, Relative-lift dependence of the action preference", "pdf_page": 306, "quote": "with the relative lift axis ∆θ unpinned, both character types admit nonzero action-critical equivariant points, so the action’s “vote” for the root line is common-lift-conditional only (casualty #5, corrected in place)." }, "caution": "The correction neither selects the relative lift axis nor contradicts the explicitly conditional root-line result.", "candidate_ids": [ "C2-105" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-262/", "content_sha256": "e53fe5e50f721e8c4557e70f52a5bb3f09e0d4e96078590bef2181473e450176", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-263", "entry_version": 7, "class": "RETIRED", "title": "Retired depth-exclusion inference from commuting charge and mass", "statement": "The earlier depth-exclusion cut treated commutation of the mass and electromagnetic charge operators as forbidding depth sourcing.", "scope": { "carrier": null, "domain": "The former exclusion of depth sourcing, not the distinction between the two finite clock labels.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix S", "section": "§7, Casualty #7: depth-exclusion cut", "pdf_page": 307, "quote": "the depth-exclusion cut retired ([M, Qem ] = 0 forbids identifying the two Z4 labels but not depth sourcing)." }, "caution": "Withdrawing the cut does not identify the two clock labels or select depth or order as the physical source.", "candidate_ids": [ "C2-068" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-029" } ], "url": "/library-v2/LIB2-263/", "content_sha256": "fdc876ff500e95fdae6beff7b6ece1b5ed9d22253dbe0715b2ad7a647fc00e5c", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-264", "entry_version": 8, "class": "RETIRED", "title": "Withdrawn claim that the promotion functional was constructed and run", "statement": "The earlier promotion-gate account said its canonical test functional was constructed and its zero set house-verified at the required operator tier.", "scope": { "carrier": null, "domain": "The overstated construction and operator-tier verification of the promotion gate, not the narrower executable recovery map or scalar-tier zero-set result.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix X", "section": "§3.3, Promotion-gate construction correction", "pdf_page": 368, "quote": "Correction to the Rev28 wording, which said the canonical test functional Spromo “is constructed” and its zero set “house-verified”." }, "caution": "The correction does not deny the executable recovery map or the qualified scalar zero-set computation, and does not assert that the gate cannot be executed.", "candidate_ids": [ "C2-067", "C2-088" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-174" }, { "type": "related_to", "target": "LIB2-005" } ], "url": "/library-v2/LIB2-264/", "content_sha256": "5f0b021acdfea48650ea83edf2dd306ccce912d45f1519ec241af43bdc224dc1", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-265", "entry_version": 7, "class": "RETIRED", "title": "Superseded Wyler-baseline route for the muon mass", "statement": "The archived muon prompts proposed identifying the muon mass with a Wyler baseline.", "scope": { "carrier": null, "domain": "The historical muon-baseline route, not the current tau-anchored ratio or its QED matching.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 2", "section": "§3.2, Authoritative charged-lepton attribution", "pdf_page": 36, "quote": "mµ follows from the algebraic ratio formula [A616, A618], re-typed Structural / Loaded-correspondence / Reproduced above and not citable as zero-parameter (Rev29 );" }, "caution": "Replacing the physical baseline does not refute a numerical Wyler evaluation or make the current loaded ratio a derivation.", "candidate_ids": [ "C2-018", "C2-056" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-265/", "content_sha256": "0a5f971bf7d35976dab0e702e74a13d136f5a8b6c254473214f0e3e0ed5e644e", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-266", "entry_version": 7, "class": "RETIRED", "title": "Superseded electromagnetic-power Wyler formula for the muon", "statement": "The archive presented an electromagnetic-power Wyler expression as a closed muon-mass formula.", "scope": { "carrier": null, "domain": "The specific historical muon formula in L259, not every Wyler-baseline title or the current ratio.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 2", "section": "§3.2, Authoritative charged-lepton attribution", "pdf_page": 36, "quote": "mµ follows from the algebraic ratio formula [A616, A618], re-typed Structural / Loaded-correspondence / Reproduced above and not citable as zero-parameter (Rev29 );" }, "caution": "The replacement does not establish that every algebraic operation in the old formula was false or that the present normalization is forced.", "candidate_ids": [ "C2-018", "C2-056" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-266/", "content_sha256": "2d6036dc82ae2aa760d75a040feff6862a328c8408654261872f5ec3b31c8b1f", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-267", "entry_version": 8, "class": "RETIRED", "title": "Superseded sub-Wyler route for the electron mass", "statement": "The archived electron prompts proposed a sub-Wyler mass route, with the proof prompt attributing it to the minimal orbit.", "scope": { "carrier": null, "domain": "The historical sub-Wyler electron route, distinct from the current empirical-Koide closure.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 2", "section": "§3.2, External Koide attribution", "pdf_page": 36, "quote": "The electron mass is determined by the external empirical relation K = 2/3 acting on that mµ chain and the measured mτ anchor [A636, A637]." }, "caution": "The current electron chain still needs the external empirical Koide rule, the measured tau anchor and the loaded muon chain.", "candidate_ids": [ "C2-020", "C2-057" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-267/", "content_sha256": "d4a4d56f96239f23a589bb8ccfc33154b4b956d50cf60b1d35f33ee13126dfec", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-268", "entry_version": 8, "class": "RETIRED", "title": "Superseded extended-Wyler route for the tau mass", "statement": "The archived tau prompts proposed an extended-Wyler mass formula, with the proof title also naming a sum of dimensions.", "scope": { "carrier": null, "domain": "The old extended-Wyler tau-mass route, not a refutation of the dimension identity named by its proof title.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 2", "section": "§3.2, External tau role in the current chain", "pdf_page": 36, "quote": "mτ is the external anchor; mµ follows from the algebraic ratio formula [A616, A618]," }, "caution": "The use of a measured tau anchor does not falsify the archived dimension identity or supply an algebra-only tau-mass prediction.", "candidate_ids": [ "C2-113" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-268/", "content_sha256": "853494e5435d07889c23e1756c24deaa767325dc96ace6ecc3625584d5947789", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-269", "entry_version": 7, "class": "RETIRED", "title": "Superseded Peirce-cylinder proposal for the tau mass", "statement": "The archive proposed obtaining the tau mass from the muon mass through a power of a Peirce-cylinder ratio.", "scope": { "carrier": null, "domain": "The specific cylinder-powered tau proposal in L262, not the separate extended-Wyler route.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 2", "section": "§3.2, External tau role in the current chain", "pdf_page": 36, "quote": "mτ is the external anchor; mµ follows from the algebraic ratio formula [A616, A618]," }, "caution": "Replacing the proposed physical formula does not exclude every cylinder relation or turn the measured tau anchor into a prediction.", "candidate_ids": [ "C2-113" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-269/", "content_sha256": "4323c28ff5834bdf39c1e4b705cfb0e5017add37d96098d415fe55becf7bcd25", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-270", "entry_version": 7, "class": "RETIRED", "title": "Superseded D-tower formula for the bottom mass", "statement": "The archived bottom-mass prompt proposed a D-tower golden-power formula as its physical mass target.", "scope": { "carrier": null, "domain": "The earlier bottom D-tower formula, not the current tau-anchored bridge.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 2", "section": "§3.6, Current bottom boundary value and offset", "pdf_page": 38, "quote": "The mb row must be quoted with its offset: mb = (7/3)mτ = 4146 MeV against PDG 2026 mb (mb ) = 4186 ± 6 MeV is −0.95% and dcmp = −6.64 (cross-scheme, no status; full precision, Rev32.9)." }, "caution": "The current bridge remains a boundary-value correspondence with a status-ineligible cross-scheme comparison, not a low-energy mass theorem.", "candidate_ids": [ "C2-021" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-270/", "content_sha256": "936f07d3b7948efb166dacac2771ef138b5d739507fb884587db32dce550c0d0", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-271", "entry_version": 8, "class": "RETIRED", "title": "Superseded pi-weighted prefactor formula for the bottom mass", "statement": "The archived numerical bottom-mass prompt proposed the prefactor sqrt(3)·r_23/42 multiplied by (π/2)^{2/3}.", "scope": { "carrier": null, "domain": "The specific prefactor-and-power formula printed in L138, not the unspecified P51 proof prompt.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 2", "section": "§3.6, Current bottom boundary value and offset", "pdf_page": 38, "quote": "The mb row must be quoted with its offset: mb = (7/3)mτ = 4146 MeV against PDG 2026 mb (mb ) = 4186 ± 6 MeV is −0.95% and dcmp = −6.64 (cross-scheme, no status; full precision, Rev32.9)." }, "caution": "The replacement is not a re-evaluation of the archived prefactor and does not supply the missing scheme-matched physical bridge.", "candidate_ids": [ "C2-021" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-271/", "content_sha256": "702044def88aed909933a653fd9585284f45953c6e4cd74de08d0baf613cff24", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-272", "entry_version": 7, "class": "RETIRED", "title": "Superseded cylinder-prefactor proof prompt for the bottom mass", "statement": "The archived proof prompt proposed deriving the bottom-mass prefactor from the Peirce cylinder.", "scope": { "carrier": null, "domain": "The physical prefactor-origin assertion in P51 at title level, without reconstructing its absent formula.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 2", "section": "§3.6, Current bottom boundary value and offset", "pdf_page": 38, "quote": "The mb row must be quoted with its offset: mb = (7/3)mτ = 4146 MeV against PDG 2026 mb (mb ) = 4186 ± 6 MeV is −0.95% and dcmp = −6.64 (cross-scheme, no status; full precision, Rev32.9)." }, "caution": "A title-level replacement does not establish that the absent prefactor proof was executed or mathematically disproved.", "candidate_ids": [ "C2-021" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-272/", "content_sha256": "1e84b7b701a82720d60adeaf05a2d5a4a8e055d94a36611c6afb7df957da668e", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-273", "entry_version": 7, "class": "RETIRED", "title": "Superseded D-tower formula for the charm mass", "statement": "The archived charm-mass prompt proposed a D-tower golden-power formula as its physical mass target.", "scope": { "carrier": null, "domain": "The earlier charm D-tower formula, distinct from the current constituent-anchored bridge.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 2", "section": "§3.6, Current charm boundary value and offset", "pdf_page": 38, "quote": "The charm bridge value mc = 1291.9 MeV lies +1.49% above the PDG 2026 MS comparator mc (mc ) = 1272.9 ± 4.5 MeV." }, "caution": "The current constituent-anchored comparison is not a scheme-matched mass theorem or a refutation of every tower construction.", "candidate_ids": [ "C2-022" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-273/", "content_sha256": "daf9aad905a9b6d49f30ad19a0181d0d2d63a22f5edc37dd79b74eebe6128dc8", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-274", "entry_version": 8, "class": "RETIRED", "title": "Superseded triality log-geometric-mean charm formula", "statement": "The archived triality proposal proposed obtaining the charm mass from a geometric combination of the muon and top masses.", "scope": { "carrier": null, "domain": "The specific L132 formula explicitly associated with P46, not all triality-based charm prompts.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 2", "section": "§3.6, Current charm boundary value and offset", "pdf_page": 38, "quote": "The charm bridge value mc = 1291.9 MeV lies +1.49% above the PDG 2026 MS comparator mc (mc ) = 1272.9 ± 4.5 MeV." }, "caution": "The current target replaces this physical formula without proving that every triality identity in its absent derivation was false.", "candidate_ids": [ "C2-022" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-274/", "content_sha256": "61d3a2d4b1010b86487765bc18a3b5d740d1ec8d18e00f19f4216d5c44770403", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-275", "entry_version": 7, "class": "RETIRED", "title": "Superseded cubic-to-tower triality bridge for the charm mass", "statement": "The archived charm proof prompt proposed a triality bridge from the Jordan cubic to a D-tower.", "scope": { "carrier": null, "domain": "The historical P29 cubic-to-D-tower construction at title level, not the separately specified log-geometric-mean formula.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 2", "section": "§3.6, Current charm boundary value and offset", "pdf_page": 38, "quote": "The charm bridge value mc = 1291.9 MeV lies +1.49% above the PDG 2026 MS comparator mc (mc ) = 1272.9 ± 4.5 MeV." }, "caution": "The title-level replacement neither reconstructs the old cubic bridge nor makes the current physical mass export a theorem.", "candidate_ids": [ "C2-022" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-275/", "content_sha256": "9ace8ab9175f1be26711539219e911b0c66a81de1e823fc8ff308125b2c0ed47", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-276", "entry_version": 7, "class": "RETIRED", "title": "Superseded resummed-electromagnetic charm formula", "statement": "The archived charm prompt proposed obtaining its mass from the top mass and a resummed electromagnetic-coupling factor.", "scope": { "carrier": null, "domain": "The specific electromagnetic-resummation charm formula of P67, not the current constituent-anchored bridge.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 2", "section": "§3.6, Current charm boundary value and offset", "pdf_page": 38, "quote": "The charm bridge value mc = 1291.9 MeV lies +1.49% above the PDG 2026 MS comparator mc (mc ) = 1272.9 ± 4.5 MeV." }, "caution": "Replacing this formula does not establish a general electromagnetic-resummation no-go or complete the present mass-scheme conversion.", "candidate_ids": [ "C2-022" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-276/", "content_sha256": "66dca5d974252a5eaa6c10cfbf6d6bb6610bbae0d308c0e09ffc30a603c3a327", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-277", "entry_version": 8, "class": "RETIRED", "title": "Superseded early cubic-phase ansatz for the leptonic Dirac phase", "statement": "The early PMNS phase prompts proposed a cubic-invariant ansatz as the leptonic Dirac-phase target; the current print types δCP = −2π/√5 = −160.997° Derived-conditional (Rev29 re-tiering; the pre-Rev29 stamp was Theorem ⋆100).", "scope": { "carrier": null, "domain": "The old bare ansatz target, including only the bare-target clause of L256, not a reconstructed torsion correction.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 7", "section": "§7, D4 closed: old ansatz superseded", "pdf_page": 120, "quote": "The old ansatz value −133.36◦ is superseded." }, "caution": "The new target remains conditional on its readout premises; replacement does not prove that the archived prompt contained a completed derivation.", "candidate_ids": [ "C2-007", "C2-061" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-277/", "content_sha256": "ee4ffe5f305b235afa3de4ffb2da25339a0566a769b971b0342c55f3f79a5d2d", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-278", "entry_version": 8, "class": "RETIRED", "title": "Superseded imaginary-correction prompt for the leptonic phase", "statement": "The archived numerical prompt proposed an imaginary-correction term to adjust the leptonic Dirac phase toward a benchmark; the current print types δCP = −2π/√5 = −160.997° Derived-conditional (Rev29 re-tiering; the pre-Rev29 stamp was Theorem ⋆100).", "scope": { "carrier": null, "domain": "The imaginary-correction proposal in L135, not the retained V3 readout or the separate class-algebra cross-check.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 5", "section": "§3, Retained leptonic-phase readout", "pdf_page": 88, "quote": "δCP = −2π/ 5 = −160.997◦" }, "caution": "Replacing this correction prompt does not derive the physical readout map or establish a universal exclusion of phase corrections.", "candidate_ids": [ "C2-007", "C2-061" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-278/", "content_sha256": "1061b28b53a98e0ca999c40bdc5a9c1b31b39ce61198041b6a1a13eb671e3dd9", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-279", "entry_version": 8, "class": "RETIRED", "title": "Superseded determinant-imaginary-part route for the full leptonic phase", "statement": "The archived extension prompt proposed obtaining the full leptonic Dirac phase from the imaginary part of the Jordan determinant; the current print types δCP = −2π/√5 = −160.997° Derived-conditional (Rev29 re-tiering; the pre-Rev29 stamp was Theorem ⋆100).", "scope": { "carrier": null, "domain": "The proposed full-phase extraction of P48, not the old bare ansatz value or a theorem that every determinant invariant vanishes.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 5", "section": "§3, Retained leptonic-phase readout", "pdf_page": 88, "quote": "δCP = −2π/ 5 = −160.997◦" }, "caution": "This replacement neither reconstructs the absent determinant-phase proof nor removes the conditions on the current phase attachment.", "candidate_ids": [ "C2-007", "C2-061" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-279/", "content_sha256": "047768b207d4565a4c5fb41e6f74e24c53fc290e814cfe906de211d1cc2b3da5", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-280", "entry_version": 8, "class": "RETIRED", "title": "Superseded sum-rule and torsion-corrected reactor route to the leptonic phase", "statement": "The archived phase prompt proposed a sum-rule readout using a torsion-corrected reactor angle; the current print types δCP = −2π/√5 = −160.997° Derived-conditional (Rev29 re-tiering; the pre-Rev29 stamp was Theorem ⋆100).", "scope": { "carrier": null, "domain": "The proposed phase construction in P66, not the independent status of the sum rule or every possible torsion correction.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 5", "section": "§3, Retained leptonic-phase readout", "pdf_page": 88, "quote": "δCP = −2π/ 5 = −160.997◦" }, "caution": "The replacement does not refute an unspecified sum-rule identity or turn the current reactor and phase readouts into unconditional predictions.", "candidate_ids": [ "C2-007", "C2-061" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-280/", "content_sha256": "61ab7e953fc400d36aaf09173ebd153580e71672165f27a4a7ec7bef08a0e191", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-281", "entry_version": 7, "class": "RETIRED", "title": "Superseded cylinder formula for the reactor angle", "statement": "The archived reactor-angle prompt proposed an electromagnetic-power arctangent from the Peirce cylinder as its mixing-angle target.", "scope": { "carrier": null, "domain": "The specific L133 cylinder formula and its explicitly named P45 proof prompt, not the later torsion-corrected variant.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 5", "section": "§2, Retained reactor-angle expression", "pdf_page": 83, "quote": "sin2 θ13 = sin4 (π/8)" }, "caution": "The current reactor expression retains an unforced readout premise; replacing the older target does not prove a universal cylinder-model exclusion.", "candidate_ids": [ "C2-006", "C2-060" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-281/", "content_sha256": "4ab40033117bf90a9a353bacf693f8d8e3ab15659046f189df8e824b671da059", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-282", "entry_version": 7, "class": "RETIRED", "title": "Superseded torsion-corrected cylinder formula for the reactor angle", "statement": "The archived reactor-angle proof prompt advertised an exact target obtained by subtracting a torsion correction from the cylinder arctangent.", "scope": { "carrier": null, "domain": "The torsion-corrected physical formula of P65, distinct from the uncorrected L133/P45 proposal.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 5", "section": "§2, Retained reactor-angle expression", "pdf_page": 83, "quote": "sin2 θ13 = sin4 (π/8)" }, "caution": "This replacement does not establish the old correction's value or make the current readout rule canonical.", "candidate_ids": [ "C2-006", "C2-060" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-282/", "content_sha256": "d419c0614b29542362fd1188690a013d1d1216a3378a7c5e6f5610a113f6ece2", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-283", "entry_version": 7, "class": "RETIRED", "title": "Superseded torsion-corrected PMNS angle scheme", "statement": "The archived PMNS-angle prompt proposed a torsion-corrected scheme combining quark–lepton complementarity, Shilov and split-G2 contributions.", "scope": { "carrier": null, "domain": "The named composite angle scheme at title level, not reconstructed individual formulas for its absent historical angle set.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 5", "section": "§2, Current PMNS angle provenance", "pdf_page": 83, "quote": "current: θ12 , δCP Derived-conditional, the physical θ23 octant Loaded-correspondence — A1566" }, "caution": "The current mixed-provenance angle set does not refute every torsion correction or derive the physical readout and octant choices.", "candidate_ids": [ "C2-004", "C2-005", "C2-006", "C2-058", "C2-059", "C2-060" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-283/", "content_sha256": "19192d0c21a8fa70bfee6613e867df8620f7475dfedda2bb49d162cf51387e0b", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-284", "entry_version": 7, "class": "RETIRED", "title": "Superseded Shilov-circle correction prompt for the atmospheric angle", "statement": "The archived atmospheric-angle proof prompt proposed a Shilov-circle correction as its physical angle construction.", "scope": { "carrier": null, "domain": "The physical construction named by P40, without identifying its absent formula with the separately archived arctangent or rational targets.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 7", "section": "§7, Atmospheric-angle precedent", "pdf_page": 120, "quote": "The current framework value is the mismatch-geometry branch sin2 θ23 = 7/16, rather than the older higher-octant phenomenological placeholder" }, "caution": "The present lower-octant target is a loaded correspondence, and this replacement does not refute every Shilov-circle identity.", "candidate_ids": [ "C2-005", "C2-059" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-284/", "content_sha256": "c96c9c584345d08beccaa1c7e48e2cb47f73d016a685534ba3eb91ea1732d9cf", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-285", "entry_version": 8, "class": "RETIRED", "title": "Superseded Peirce golden-power assignment for two CKM magnitudes", "statement": "The archived Peirce-sector proposal assigned V_cb = λ²/φ and V_ub = λ³/φ, successive powers of the same λ divided by the golden ratio.", "scope": { "carrier": null, "domain": "The paired scaling assignment printed in L129, not a universal CKM construction or its absent choice of the common parameter.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix B", "section": "§B.6, Current CKM magnitude provenance", "pdf_page": 162, "quote": "first row Loaded, |Vcb | Loaded-correspondence attach- ment (physical) / Structural formula" }, "caution": "The current magnitude formulas remain loaded and do not derive the physical CKM matrix from the bare algebra.", "candidate_ids": [ "C2-010", "C2-011", "C2-063", "C2-064" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-285/", "content_sha256": "a08abebc39f57ff63894f98d832df49fbcb58e96b75f5bd201e31a985bb3c1ea", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-286", "entry_version": 8, "class": "RETIRED", "title": "Superseded additive correction prompt for Vcb", "statement": "The archived numerical prompt proposed a correction to the Vcb target using its beta-delta coefficient.", "scope": { "carrier": null, "domain": "The particular numerical correction proposed in L137, not an adjudication of the standalone coefficient or every correction to Vcb.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix B", "section": "§B.6, Retained Vcb formula", "pdf_page": 162, "quote": "|Vcb | 1/(9 7) = 0.041996" }, "caution": "The replacement does not derive the current integer choice or establish that every proposed correction is excluded.", "candidate_ids": [ "C2-010", "C2-063" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-286/", "content_sha256": "8b3e6f66a39d415738d6dd37ce90077fc61ffc537f42717181b645b448155a86", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-287", "entry_version": 7, "class": "RETIRED", "title": "Superseded golden-power ratio of CKM hierarchy magnitudes", "statement": "The archived hierarchy proposals identified the Vub-to-Vcb magnitude ratio with a fixed negative power of the golden ratio.", "scope": { "carrier": null, "domain": "Only the displayed Vub/Vcb relation of L282 and L294; the separate Rb assertion in L282 is not retired by this record.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix B", "section": "§B.6, Retained Vub hierarchy relation", "pdf_page": 162, "quote": "|Vub | |Vus ||Vcb |/ 6 = 0.003862" }, "caution": "This replaces the physical hierarchy ratio only and leaves the separate Rb subclaim unadjudicated.", "candidate_ids": [ "C2-011", "C2-064" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-287/", "content_sha256": "af27731405e0a83d8b7296e428c008e4fdecc3ae24e4ec4b3a2fc61c27a31551", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-288", "entry_version": 7, "class": "RETIRED", "title": "Superseded Cabibbo-squared formula for Vcb", "statement": "The archived proof prompt proposed obtaining Vcb from the squared sine of a corrected Cabibbo angle divided by the square root of the golden ratio.", "scope": { "carrier": null, "domain": "The P68 corrected-Cabibbo formula, not the distinct lambda-power assignment of L129.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix B", "section": "§B.6, Retained Vcb formula", "pdf_page": 162, "quote": "|Vcb | 1/(9 7) = 0.041996" }, "caution": "Replacing this historical formula does not select the present physical attachment or the unforced integer in its denominator.", "candidate_ids": [ "C2-010", "C2-063" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-288/", "content_sha256": "b7b590373fa19787615d7e3684818d497cd61e822f3f0c900d17d3739497f700", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-289", "entry_version": 8, "class": "RETIRED", "title": "Superseded reciprocal weak-angle proposal", "statement": "The archived weak-angle prompt proposed the reciprocal expression sin²θ_W = 1/(2+φ) as its physical target.", "scope": { "carrier": null, "domain": "The reciprocal target of L127, not the retained Peirce weak-angle identity or its unresolved scheme matching.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 4", "section": "§7, Current weak-angle target and precision boundary", "pdf_page": 77, "quote": "We therefore carry ϕ−3 as a ∼ 2% structural tree-level target on the electroweak curve, not as a completed Z-pole precision prediction." }, "caution": "The current weak-angle target still requires its independent polarization premise and a derived matching scale.", "candidate_ids": [ "C2-014" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-289/", "content_sha256": "fbcb0ee409ee2f0a02576813a2c0c9c2fac578d59ce551807d6a83a6d48f53b1", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-290", "entry_version": 7, "class": "RETIRED", "title": "Superseded logarithmic loop-correction prompt for the weak angle", "statement": "The archived numerical prompt proposed a logarithmic one-loop correction to adjust the weak-angle value toward its comparator.", "scope": { "carrier": null, "domain": "The logarithmic correction in L134, without assigning the missing numerical placeholders or identifying it with the separate P47 prompt.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 4", "section": "§7, Current weak-angle target and precision boundary", "pdf_page": 77, "quote": "We therefore carry ϕ−3 as a ∼ 2% structural tree-level target on the electroweak curve, not as a completed Z-pole precision prediction." }, "caution": "The current scope does not exclude every electroweak loop correction or provide the missing scale and threshold calculation.", "candidate_ids": [ "C2-014" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-290/", "content_sha256": "022b1f1b8ea9383d73288cb6e643d933cdd4a0911b406bab4ed9bcad0f8e3b07", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-291", "entry_version": 7, "class": "RETIRED", "title": "Superseded cylinder-running proof prompt for the weak angle", "statement": "The archived proof prompt proposed obtaining the weak angle from one-loop Peirce-cylinder running.", "scope": { "carrier": null, "domain": "The physical running construction named in P47, not an unspecified equation imported from a neighbouring archive title.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 4", "section": "§7, Current weak-angle target and precision boundary", "pdf_page": 77, "quote": "We therefore carry ϕ−3 as a ∼ 2% structural tree-level target on the electroweak curve, not as a completed Z-pole precision prediction." }, "caution": "The replacement does not refute all cylinder-running models or derive a completed Z-pole prediction.", "candidate_ids": [ "C2-014" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-291/", "content_sha256": "640c66b0dce2e9b4c1d8ac96edc809b010c5dd44702d638f77fc9de8651ded8e", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-292", "entry_version": 7, "class": "RETIRED", "title": "Superseded electromagnetic-subtraction formula for the weak angle", "statement": "The archived weak-angle proof prompt proposed an electromagnetic subtraction from the golden tree target as a one-loop correction.", "scope": { "carrier": null, "domain": "The specific subtraction formula in P70, distinct from the logarithmic and cylinder-running proposals.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 4", "section": "§7, Current weak-angle target and precision boundary", "pdf_page": 77, "quote": "We therefore carry ϕ−3 as a ∼ 2% structural tree-level target on the electroweak curve, not as a completed Z-pole precision prediction." }, "caution": "The current structural target is not a completed radiative prediction, and the replacement does not exclude all electromagnetic corrections.", "candidate_ids": [ "C2-014" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-292/", "content_sha256": "669902cfadee67974a9941d4ff88e06d93500eee42454e0700305001af0b57f6", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-293", "entry_version": 8, "class": "RETIRED", "title": "Superseded QLC-plus-cylinder correction for the Cabibbo angle", "statement": "The archived numerical prompt proposed Δθ_C = arctan(α^{1/3}/(r₁₂/v)) and an adjusted Cabibbo value θ_C = QLC + Δ.", "scope": { "carrier": null, "domain": "The adjusted Cabibbo construction in L136, not the present Route-B readout or the separate measured-solar-angle diagnostic.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 3", "section": "§2, Kernel-line exact-framework Cabibbo readout", "pdf_page": 49, "quote": "the canonical current value is |Vus | = 0.225256 √ (the exact framework angle arctan( 3/ϕ2 ) = 33.4880◦ , printed from the kernel line s1162;" }, "caution": "The current framework-angle readout remains route-selected by data and does not derive the physical first-row map.", "candidate_ids": [ "C2-009", "C2-062" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-293/", "content_sha256": "6a89b6dc957d8fcb1aa755e822e6be7d33c3417e3a9eb8d827595ce7f23b58ac", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-294", "entry_version": 7, "class": "RETIRED", "title": "Superseded torsion-corrected Cabibbo–Weinberg formula", "statement": "The archived Cabibbo proof prompt proposed an arctangent of the golden weak-angle expression followed by a torsion subtraction.", "scope": { "carrier": null, "domain": "The Cabibbo–Weinberg construction in P64, not the current independent weak-angle target and loaded first-row readout.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 3", "section": "§2, Kernel-line exact-framework Cabibbo readout", "pdf_page": 49, "quote": "the canonical current value is |Vus | = 0.225256 √ (the exact framework angle arctan( 3/ϕ2 ) = 33.4880◦ , printed from the kernel line s1162;" }, "caution": "Replacing this formula neither selects the current first-row route nor solves the weak-angle matching problem.", "candidate_ids": [ "C2-009", "C2-062" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-294/", "content_sha256": "faee1c9785c83d10177e2f1fe58e326fee63ccf134152b7de34c300b69c937a2", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-295", "entry_version": 7, "class": "RETIRED", "title": "Superseded Cabibbo–Weinberg residual identity as a physical target", "statement": "The archived proof prompt proposed equating a Cabibbo–Weinberg residual with an electromagnetic expression.", "scope": { "carrier": null, "domain": "The physical residual relation of P73, not a new test of the relation in an unspecified angle scheme or scale.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 3", "section": "§2, Kernel-line exact-framework Cabibbo readout", "pdf_page": 49, "quote": "the canonical current value is |Vus | = 0.225256 √ (the exact framework angle arctan( 3/ϕ2 ) = 33.4880◦ , printed from the kernel line s1162;" }, "caution": "The current separate readouts do not supply a scheme-matched test or a universal refutation of the old residual relation.", "candidate_ids": [ "C2-009", "C2-014", "C2-062" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-295/", "content_sha256": "fe55aa312054215d7350cad5bcde2616fbf02b6558f5ea39fd579cf95b0fdbe0", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-296", "entry_version": 8, "class": "RETIRED", "title": "Superseded singular-vacuum premise of the protection-and-bounce chain", "statement": "The archived protection-and-bounce chain assumed a vanishing determinant and a vanishing third eigenvalue at the working vacuum.", "scope": { "carrier": null, "domain": "The singular-working-vacuum premise in L278, not the entire uninspected chain of protection and bounce implications.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix I", "section": "§6, Remark 6.4: vacuum normalization supersession", "pdf_page": 219, "quote": "the legacy vacuum normalization diag(ϕ2 , 1, 0) is superseded by the current {ϕ, 1, ϕ−1 } frame, the structural statements unaffected." }, "caution": "The normalization replacement does not exclude singular Jordan elements or independently adjudicate the old Z-mass protection and bounce implications.", "candidate_ids": [ "C2-002" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-296/", "content_sha256": "4339b5ccf9ee8b10e4dd6ddd6211d95a7db473cf523bbd8f455f35ea10e0c6a5", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-297", "entry_version": 7, "class": "RETIRED", "title": "Retired compact-colour subgroup claim in the split-G2 real form", "statement": "The archived branching prompt presented compact colour as a maximal subgroup of the split-G2 real form.", "scope": { "carrier": null, "domain": "The compact-colour inclusion asserted by P28 in the named split real form, not all colour embeddings.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix N", "section": "Part N.B, Proposition 2.1: compact-colour obstruction", "pdf_page": 266, "quote": "The compact colour algebra su(3) (dimension 8) cannot embed in the compact part available to the loaded subimage, whose maximal compact dimension is 6 < 8." }, "caution": "The obstruction concerns the named split real form and does not exclude compact colour on a separately chosen carrier or real form.", "candidate_ids": [ "C2-038" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-297/", "content_sha256": "a197f5bb12edf847701e2baceb03e6bf86078ba15559cd4f85fd43509c1d2165", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-298", "entry_version": 7, "class": "RETIRED", "title": "Withdrawn physical-generation implication of the triality carrier cycle", "statement": "The archived triality title presented the cycle of vector and spinor carriers as a generation mechanism.", "scope": { "carrier": null, "domain": "The physical-family replication reading of L280, not the triality cycle itself.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 0", "section": "Generation-replication boundary", "pdf_page": 18, "quote": "algebraic replication of three generations inside a single J3 (Os ) is excluded: three families need 3 × 16 = 48 fermionic dimensions, which do not fit in the 27 (8+8+8 = 24 off-diagonal, and triality maps 8+ → 8− → 8v , so the blocks are not three gauge-identical copies) [A691]." }, "caution": "The physical replication reading is withdrawn; the triality cycle is not refuted and the discrete generation count is not derived.", "candidate_ids": [ "C2-040" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-108" } ], "url": "/library-v2/LIB2-298/", "content_sha256": "ca75f676c9f02aaaad65cb01f5ba1391c3689e5ea4a416b32a8467b6081cbae7", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-299", "entry_version": 7, "class": "OPEN", "title": "Derive the anchor relations required by the physical one-input programme", "statement": "Can derived relations with uncertainties tie the electroweak and hadronic anchors to the registered central scale class?", "scope": { "carrier": "The registered central scale class and the electroweak and hadronic anchors", "domain": "The physical linkage obligation, distinct from the abstract scale-class count and the anchor usage inventory.", "group": null, "hypotheses": [ "Retain the input-count convention and the stated registered identifications." ], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "OPEN", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix X", "section": "Registered input: physical one-input condition", "pdf_page": 352, "quote": "the physical “one-input” reading becomes available only when derived relations with uncertainties tie vEW and ΛG2 to the registered class." }, "caution": "This question does not convert the abstract scale-class theorem into a derivation of the measured anchors.", "candidate_ids": [ "C2-070", "C2-081", "C2-100" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-056" }, { "type": "related_to", "target": "LIB2-124" } ], "url": "/library-v2/LIB2-299/", "content_sha256": "cb9549fc5d32e413cb54850d53b71a92d308a1f9af4778c3e9b32a2e52713916", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-300", "entry_version": 7, "class": "OPEN", "title": "Construct the missing continuum Yang–Mills functor", "statement": "Can the programme construct its missing continuum Yang–Mills functor beyond the finite categorical and Gaussian checkpoints?", "scope": { "carrier": "The finite cluster construction and the continuum staging programme", "domain": "The unbuilt continuum map, not the finite winding functor or toy resolvent.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "OPEN", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 9", "section": "Posture: missing continuum object", "pdf_page": 129, "quote": "The continuum (Yang–Mills) functor remains the named missing object: nothing in this paper is a Clay-problem claim." }, "caution": "No continuum existence theorem, physical propagator or Clay-problem result is claimed.", "candidate_ids": [ "C2-084" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-143" }, { "type": "related_to", "target": "LIB2-165" }, { "type": "related_to", "target": "LIB2-166" } ], "url": "/library-v2/LIB2-300/", "content_sha256": "927ba8e67993ea287dccf0f0c867412f4407dc370bf12d0c5dae96f4abf83aec", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-301", "entry_version": 7, "class": "OPEN", "title": "Test Einstein universality of the finite-regulator gravity construction", "statement": "Does the sourced heat-kernel action yield an AdS linearized spectrum consistent with linearized general relativity?", "scope": { "carrier": "The sourced heat-kernel action and its constrained gravitational sector", "domain": "The universality test beyond finite-regulator measure existence.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "OPEN", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix T", "section": "§8, Theorem 8.6: remaining Einstein object", "pdf_page": 324, "quote": "Einstein universality — the AdS linearized spectrum of the sourced heat-kernel action — is the remaining named object." }, "caution": "The existence of a positive measure at finite regulator is not an Einstein-universality result.", "candidate_ids": [ "C2-087" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-170" }, { "type": "related_to", "target": "LIB2-172" }, { "type": "related_to", "target": "LIB2-189" }, { "type": "related_to", "target": "LIB2-192" } ], "url": "/library-v2/LIB2-301/", "content_sha256": "0ad4b04ac121c07b023837245b5737a5b473a70e41ca0ade8abb1609b104cff3", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-302", "entry_version": 7, "class": "OPEN", "title": "Construct the normalized physical mass-response map", "statement": "Can the normalized response into the mass quadrature be constructed with an interacting LSZ or self-energy attachment and dimensional registration?", "scope": { "carrier": "The mass quadrature and its unbuilt normalized physical response", "domain": "The interacting physical mass attachment, distinct from the quasi-free gap and the joint basepoint/output-map task.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "OPEN", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix T", "section": "§8, Theorem 8.11: named mass-response map", "pdf_page": 325, "quote": "The named missing object is Nmass : a normalized physical response map into the mass quadrature, with LSZ/self-energy attachment and dimensional registration." }, "caution": "No interacting rest mass, physical occupancy or repair of the exact single-χ ratio failure is asserted.", "candidate_ids": [ "C2-090" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-193" }, { "type": "related_to", "target": "LIB2-106" }, { "type": "related_to", "target": "LIB2-186" }, { "type": "related_to", "target": "LIB2-005" } ], "url": "/library-v2/LIB2-302/", "content_sha256": "43fe8f213f15546870638012a60538c4950cb1ac30f1686ceabf9377b69bc41b", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-303", "entry_version": 7, "class": "OPEN", "title": "Construct the packing or coordination explanation of the deficit window", "statement": "Can a packing or coordination mechanism account for the six-to-seven-cell binding deficit outside the excluded annular-repair class?", "scope": { "carrier": "The six-to-seven-cell cluster deficit", "domain": "The surviving packing/coordination class for the binding residual, not the separate forked silicon readout.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "OPEN", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 9", "section": "§9, Reopen class of the six-to-seven-cell deficit", "pdf_page": 137, "quote": "The reopen class is therefore packing/coordination of 6–7 cells (writhe sector), not “annular second order”; the negative-annular closure (A1545 T4) stands." }, "caution": "Naming packing or coordination is not a completed mechanism, and this task does not resolve the distinct silicon readout fork.", "candidate_ids": [ "C2-083", "C2-128" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-154" }, { "type": "related_to", "target": "LIB2-156" }, { "type": "related_to", "target": "LIB2-157" }, { "type": "related_to", "target": "LIB2-158" }, { "type": "related_to", "target": "LIB2-159" } ], "url": "/library-v2/LIB2-303/", "content_sha256": "57dc1f194fe4f2c50a2991a36c9a0b8a2fa54739b1769d080ec287bc20d76fa3", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-304", "entry_version": 7, "class": "OPEN", "title": "Derive the configuration-dependent charge-magnitude mechanism", "statement": "Can configuration-dependent coherence and screening supply the missing nuclear charge magnitudes under the banked separation-energy baseline?", "scope": { "carrier": "The nuclear charge sector and refined parent/daughter ledger", "domain": "The unresolved charge-magnitude mechanism, distinct from the sign/count record and binding-energy pass tally.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "OPEN", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 9", "section": "§9, Coherence mechanism is not yet a solution", "pdf_page": 137, "quote": "The banked candidate mechanism — coherence factors are configuration-dependent (“coherence multiplies by φ”) — names the problem without solving it." }, "caution": "The strong sign/count record does not establish the magnitude law or license a more favourable baseline.", "candidate_ids": [ "C2-072" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-155" }, { "type": "related_to", "target": "LIB2-163" } ], "url": "/library-v2/LIB2-304/", "content_sha256": "d0008a372988b5a4a7126c350150a03a45fdde05960122a369989952a7549331", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-305", "entry_version": 7, "class": "OPEN", "title": "Supply the missing QCD flip energy in the neutron–proton splitting", "statement": "Can a QCD flip energy complete the neutron–proton mass-difference calculation alongside the existing Coulomb/QED contribution?", "scope": { "carrier": "The QCD flip contribution and the existing Coulomb/QED term", "domain": "The unpriced physical neutron–proton difference, not the selected isospin Casimir coefficient.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "OPEN", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 9", "section": "§9, Isospin sector: unpriced neutron–proton difference", "pdf_page": 138, "quote": "The neutron–proton mass difference mn − mp = 1.2933 MeV is unpriced: the framework carries the QED half (Coulomb, with α external) and no QCD half (mu = md at constituent level; the e7 flip carries no energy), so without a flip energy its sign comes out wrong (s1129)." }, "caution": "No neutron–proton mass prediction or continuous isospin dynamics follows from the registered parity alone.", "candidate_ids": [ "C2-130" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-160" }, { "type": "related_to", "target": "LIB2-161" }, { "type": "related_to", "target": "LIB2-304" } ], "url": "/library-v2/LIB2-305/", "content_sha256": "d3679502657fdfa424f5dec97e1b95ab8163e18668cf54e29001f133b8714e01", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-306", "entry_version": 7, "class": "OPEN", "title": "Resolve the parent breathing-mode accounting", "statement": "Is the registered breathing excitation present in the A = 8 parent typings used in the separation-energy ledger?", "scope": { "carrier": "The breathing excitation and the A = 8 parent/daughter typings", "domain": "The open naturality check on parent and daughter excitation content, not a new energy correction.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "OPEN", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 9", "section": "§9, Open breathing-accounting audit", "pdf_page": 138, "quote": "Whether ∆br is present in the A = 8 parents is an unchecked naturality square:" }, "caution": "The existence of the breathing generator does not establish its presence in every parent or a revised separation energy.", "candidate_ids": [ "C2-072", "C2-075" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-162" }, { "type": "related_to", "target": "LIB2-163" }, { "type": "related_to", "target": "LIB2-304" } ], "url": "/library-v2/LIB2-306/", "content_sha256": "69f05da0e1f62ff0cef5edc3e565c2d717e9cbf11a249497eaa7ebd4100b611b", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-307", "entry_version": 7, "class": "OPEN", "title": "Construct the interacting chiral determinant-line trivialization", "statement": "Can the interacting chiral determinant line be trivialized in a gauge-invariant, reflection-compatible and globally phase-consistent way?", "scope": { "carrier": "The interacting chiral determinant line", "domain": "The interacting chiral measure, distinct from the registered free-sector determinant calculation.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "OPEN", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix T", "section": "§7, Proposition 7.5: interacting chiral boundary", "pdf_page": 322, "quote": "the free sector is closed, the interacting chiral sector is open." }, "caution": "The free determinant and anomaly checks do not establish a positive interacting chiral measure.", "candidate_ids": [ "C2-094" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-188" }, { "type": "related_to", "target": "LIB2-109" }, { "type": "related_to", "target": "LIB2-170" } ], "url": "/library-v2/LIB2-307/", "content_sha256": "59ba5b3392fa89b6125cfb6a4795233f68881b534b9633ba18d0c8a9b325a49f", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-308", "entry_version": 7, "class": "OPEN", "title": "Derive the sign that selects the atmospheric-octant registration", "statement": "Can a registered odd coupling with a theory-fixed sign exclude the mirror atmospheric-octant registration without using the target angle, phase or observed charge-sign data?", "scope": { "carrier": "The chirality and octant torsors and a prospective odd coupling", "domain": "The physical octant-sign selection, not the internal mismatch identity.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "OPEN", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix N", "section": "Part N.E, Atmospheric-octant reopen condition", "pdf_page": 269, "quote": "a registered loaded odd object Ω23 with a theory-fixed sign in a coupling such as Slink = −κ χodd cos 2θ23 , plus a pre-registered mirror control proving the countermap impossible without using θ23 , δ, or observed charge-sign data." }, "caution": "An odd carrier alone does not derive the physical lower-octant attachment or alter the internal mismatch identity.", "candidate_ids": [ "C2-005", "C2-059" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-002" }, { "type": "related_to", "target": "LIB2-100" }, { "type": "related_to", "target": "LIB2-241" } ], "url": "/library-v2/LIB2-308/", "content_sha256": "d4eab82722231d4e77e2ed5e0507e7c19e1c9f7dd568eda8e4b616ec379369eb", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-309", "entry_version": 7, "class": "OPEN", "title": "Derive one source law for the real ladder step and compact phase", "statement": "Can one source law fix both a real ladder step and a nonzero commuting compact phase without choosing the angle after comparison?", "scope": { "carrier": "The real ladder scaling and a commuting compact datum", "domain": "The unselected joint scaling/phase law on the registered carriers, not an abstract existence claim for compact subalgebras.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "OPEN", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix N", "section": "Part N.E, Typed missing complex-ratio operator", "pdf_page": 270, "quote": "The missing object is typed: QL = SL eαJL with (JL |E )2 = −IE and [JL |E , SL |E ] = 0 on the ladder two-plane E, with E and its orientation named by the registering datum (as the antecedent D1247 states the target “on the ladder 2-plane”), and one source law fixing both the real rung step and a nonzero α; installing JL , choosing the angle, or selecting after comparison does not qualify." }, "caution": "Compact subalgebra existence and a shared spectral number do not supply a selected phase-bearing ladder operator.", "candidate_ids": [ "C2-104" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-015" }, { "type": "related_to", "target": "LIB2-101" }, { "type": "related_to", "target": "LIB2-102" }, { "type": "related_to", "target": "LIB2-103" } ], "url": "/library-v2/LIB2-309/", "content_sha256": "6770e7674e88db3e39f87cf0f21d9d5f4f7e5ae2eca50125edcd3936d8c41efe", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-310", "entry_version": 7, "class": "OPEN", "title": "Derive the scheme-specific weak-angle matching bridge", "statement": "Can the structural weak-angle target be connected to the Z-pole observable by a first-principles matching scale or a completed radiative bridge?", "scope": { "carrier": "The structural weak-angle target and its physical matching prescription", "domain": "The physical scale, scheme and threshold bridge, distinct from the independent polarization postulate.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "OPEN", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 4", "section": "§7, Running-scale and radiative-shift boundary", "pdf_page": 77, "quote": "as a running value the matching scale µ⋆ is scheme-dependent and undetermined; (ii) as a tree value bridged by standard electroweak radiative corrections, the required shift is not uniquely fixed" }, "caution": "No matching scale is selected here, and the structural target is not promoted to an electroweak precision prediction.", "candidate_ids": [ "C2-014" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-199" }, { "type": "related_to", "target": "LIB2-200" } ], "url": "/library-v2/LIB2-310/", "content_sha256": "c9006a89f3b29b5ff5a5f2a7bd7d04f167a12171f71e60b54b5353f98ece19a4", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-311", "entry_version": 7, "class": "OPEN", "title": "Find a non-residue physical realization of the finite index normalization", "statement": "Can the finite 7/3 index normalization acquire a physical realization through a non-residue, index-theoretic exceptional-field-theory construction?", "scope": { "carrier": "The finite trace/index normalization and a possible exceptional-field-theory realization", "domain": "The non-residue physical export of the finite trace/index result, outside the excluded metric-weighted residue route.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "OPEN", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix I", "section": "§8, Amplitude-bridge boundary: surviving question", "pdf_page": 222, "quote": "What stays open is only whether a non-residue, index-theoretic exceptional-field-theory realization exists; the 7 survives as the finite-carrier index (Appendix K), not as a signed amplitude." }, "caution": "The finite index theorem is not itself a low-energy mass relation, and the signed-residue route remains excluded.", "candidate_ids": [ "C2-044", "C2-054" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-053" }, { "type": "related_to", "target": "LIB2-107" }, { "type": "related_to", "target": "LIB2-130" }, { "type": "related_to", "target": "LIB2-131" } ], "url": "/library-v2/LIB2-311/", "content_sha256": "5a34f41f495ac921569b110b26094224b18deab2708b156b029877b55151893b", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-312", "entry_version": 7, "class": "OPEN", "title": "Supply a scheme-matched physical comparison for the top tree estimate", "statement": "Can the top-quark tree estimate be given a scheme-matched physical comparison through a derived matching prescription with quantified uncertainties?", "scope": { "carrier": "The top tree-level Yukawa/EW boundary value and its direct/MC mass comparator", "domain": "The physical interpretation and matching of the top tree estimate, not the internal unit Yukawa weight.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "OPEN", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix X", "section": "Honest precision summary: missing conversion with uncertainty", "pdf_page": 345, "quote": "no such conversion with uncertainty is currently supplied for these rows." }, "caution": "This task does not turn the tree estimate into a pole mass or establish a statistically meaningful mass discrepancy.", "candidate_ids": [ "C2-017" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-120" }, { "type": "related_to", "target": "LIB2-121" }, { "type": "related_to", "target": "LIB2-132" }, { "type": "related_to", "target": "LIB2-220" } ], "url": "/library-v2/LIB2-312/", "content_sha256": "670493608a4183688b1655baaf1bb27f60530f542768ed43858e4c541fc3cf55", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-313", "entry_version": 7, "class": "OPEN", "title": "Derive physical matching for the tau-anchored bottom bridge", "statement": "Can the tau-pole-anchored bottom bridge be connected to the MS-bar bottom mass at its self-scale through an explicit physical matching relation with uncertainties?", "scope": { "carrier": "The tau-pole-anchored bottom bridge and the bottom self-scale running mass", "domain": "The scheme-specific physical export of the bottom bridge, not a pole-mass conversion applied to an algebraic bridge.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "OPEN", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix X", "section": "Scheme-label declaration: bottom bridge is not a pole mass", "pdf_page": 346, "quote": "it is not a bottom pole mass, and no pole→ MS conversion is applied" }, "caution": "A matching construction is not supplied, and the finite index alone does not establish a low-energy bottom-mass relation.", "candidate_ids": [ "C2-021" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-130" }, { "type": "related_to", "target": "LIB2-132" }, { "type": "related_to", "target": "LIB2-219" }, { "type": "related_to", "target": "LIB2-311" } ], "url": "/library-v2/LIB2-313/", "content_sha256": "34e1a82ac347e8c1d435a94419230f8b8b85aa838599b39fba02989d833f648f", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-314", "entry_version": 7, "class": "OPEN", "title": "Derive the constituent-to-running-mass bridge for charm", "statement": "Can the constituent-anchored charm bridge be matched to the MS-bar charm mass at its self-scale with an explicit conversion and scheme uncertainty?", "scope": { "carrier": "The constituent-anchored charm bridge and the charm self-scale running mass", "domain": "The constituent-to-running-mass conversion for charm, not the tau-anchored bottom bridge.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "OPEN", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 2", "section": "§3.6, Missing constituent-to-MS conversion", "pdf_page": 38, "quote": "the bridge is constituent- anchored and no constituent-to-MS conversion or scheme uncertainty is supplied;" }, "caution": "The constituent proxy and exact index normalization do not by themselves determine a scheme-matched charm mass.", "candidate_ids": [ "C2-022" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-129" }, { "type": "related_to", "target": "LIB2-131" }, { "type": "related_to", "target": "LIB2-132" }, { "type": "related_to", "target": "LIB2-218" }, { "type": "related_to", "target": "LIB2-311" } ], "url": "/library-v2/LIB2-314/", "content_sha256": "d9fec31eb29be400763a6f3a7cfeb5185b9a7f008aef0b80e1266561df50842f", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-315", "entry_version": 7, "class": "OPEN", "title": "Force the reactor-angle readout rather than choose its normalization", "statement": "Can the unit-endpoint-ray readout and round-trip squaring that define the reactor-angle target be forced from first principles?", "scope": { "carrier": "The Route-B endpoint readout and round-trip framing", "domain": "The unforced reactor readout rule, distinct from the symplectic moment identity and the retained numerical target.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "OPEN", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix B", "section": "Lemma B.5′, Conditional readout status", "pdf_page": 159, "quote": "it is a theorem given the unit-endpoint-ray readout rule, but that readout rule is not itself derived from the algebra" }, "caution": "The finite moment law does not independently derive the physical reactor-angle attachment.", "candidate_ids": [ "C2-006", "C2-060" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-061" }, { "type": "related_to", "target": "LIB2-252" } ], "url": "/library-v2/LIB2-315/", "content_sha256": "ead2a797ebef9a4b85539bb4a3109cb1aae7269c93510608aa9f57106c6aa030", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-316", "entry_version": 7, "class": "OPEN", "title": "Select the invariant required by the CKM-phase construction", "statement": "Can a registered operator select the eigenvalue or invariant required by the retained CKM-phase construction without assuming the correction whose origin is to be derived?", "scope": { "carrier": "The proposed operator or invariant underlying G7 in the retained CKM-phase readout", "domain": "The missing selection of G7, not an identity following from a chosen correction or another numerical menu search.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "OPEN", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 3", "section": "Candidate Construction 2.1, Operator-based reopen condition", "pdf_page": 54, "quote": "reopen only by a registered operator whose eigenvalue or invariant is G7 ." }, "caution": "An algebraic identity after choosing a correction does not select that correction or derive the physical CKM phase.", "candidate_ids": [ "C2-012", "C2-065" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-068" }, { "type": "related_to", "target": "LIB2-075" }, { "type": "related_to", "target": "LIB2-253" } ], "url": "/library-v2/LIB2-316/", "content_sha256": "99c092613ee6fd73ecc02e97e0afaf0bfa98d313567a0c10f8e4566c726b5f06", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-317", "entry_version": 6, "class": "NOT_AN_ENTRY", "title": "Reference metadata for imported Standard-Model running constants", "statement": null, "scope": { "carrier": null, "domain": "The imported one-loop Standard-Model constants in the scorecard, not a new programme result.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": null, "caution": null, "candidate_ids": [ "C2-015" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-317/", "content_sha256": "e739422ac7d3b4f5a480726954d50dd3981b973d93c367681c8dafc1d676a694", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-318", "entry_version": 7, "class": "NOT_AN_ENTRY", "title": "Source hold on the Track-2 gauge-completeness gates", "statement": null, "scope": { "carrier": null, "domain": "The specific compact-embedding, module-intertwiner and symplectic-frame completeness gates named in the imported manifest.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 6", "section": "End of the current B-frame discussion; distinct scope caveat", "pdf_page": 105, "quote": "a formal theorem over arbitrary disconnected O(4, 4) frames beyond the signed-permutation class is not yet formalized." }, "caution": "This source hold neither overturns the finite computed obstructions nor adopts a domain-wide completeness theorem.", "candidate_ids": [ "C2-039" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-076" }, { "type": "related_to", "target": "LIB2-077" }, { "type": "related_to", "target": "LIB2-081" } ], "url": "/library-v2/LIB2-318/", "content_sha256": "2cc6736a51cf219481635b9fac47a3289e9e199762cb8fcb74307dc9b891e01f", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-319", "entry_version": 6, "class": "NOT_AN_ENTRY", "title": "Merge the generic measured-scale statements as input metadata", "statement": null, "scope": { "carrier": null, "domain": "The duplicate generic scale-value sentences, which do not identify a particular measured registration.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": null, "caution": null, "candidate_ids": [ "C2-071", "C2-082" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-056" }, { "type": "related_to", "target": "LIB2-124" }, { "type": "related_to", "target": "LIB2-299" } ], "url": "/library-v2/LIB2-319/", "content_sha256": "1887e0d40c1b545c061864249770e3371e97ce924782c431b8cec151eb065fa8", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-320", "entry_version": 6, "class": "NOT_AN_ENTRY", "title": "Prospective publication-test policy is not a scientific result", "statement": null, "scope": { "carrier": null, "domain": "The prospective external-prediction acceptance gate in the Track-2 publication workflow.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": null, "caution": null, "candidate_ids": [ "C2-079" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-320/", "content_sha256": "aa1ac6a7a633e86ca5141d03db9012dc0bc9941f6807df899347d65164251aac", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-321", "entry_version": 6, "class": "NOT_AN_ENTRY", "title": "Publication-evidence availability belongs in release metadata", "statement": null, "scope": { "carrier": null, "domain": "The policy separating an active claim from publication-ready proof and artifact availability.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": null, "caution": null, "candidate_ids": [ "C2-096" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-321/", "content_sha256": "d8e800b0309a9f043ddf01b1901bd3d67c1ba1b665e34dec64f9ad230026b908", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-322", "entry_version": 7, "class": "NOT_AN_ENTRY", "title": "Taxonomy and validator descriptions are schema metadata", "statement": null, "scope": { "carrier": null, "domain": "The controlled-vocabulary and manifest-validator description, not a mathematical or physical claim.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 0", "section": "Two-axis provenance: physical attachment is separate", "pdf_page": 9, "quote": "Physical attachment never inherits the mathematical tier: an exact theorem about the algebra is not, by itself, a physical prediction until its attachment is stated." }, "caution": null, "candidate_ids": [ "C2-101" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-322/", "content_sha256": "8aedfb6811fa6736f22f2d470e5530593f9268bc8478d8ceb8c1c39e7584167a", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-323", "entry_version": 7, "class": "NOT_AN_ENTRY", "title": "Boundary-condition-family ruling is premise metadata", "statement": null, "scope": { "carrier": null, "domain": "The PI's choice of the primary boundary-condition family and the conditional or deferred alternatives.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix E", "section": "Three PI rulings printed beside the closure, S284.1", "pdf_page": 177, "quote": "The boundary-condition-family question is ruled: CLASS-ρ is primary; CLASS-W applies under C4 = 0; CLASS-H is deferred." }, "caution": null, "candidate_ids": [ "C2-115" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-030" }, { "type": "related_to", "target": "LIB2-031" }, { "type": "related_to", "target": "LIB2-032" } ], "url": "/library-v2/LIB2-323/", "content_sha256": "28b9d076b82873f11d1b49a132d699515b32d708cf0e845ca668ea893c1e363b", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-324", "entry_version": 7, "class": "NOT_AN_ENTRY", "title": "SEL-27 declaration status is workflow metadata", "statement": null, "scope": { "carrier": null, "domain": "The PI-declaration status after the scoped selection-inventory closure.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix E", "section": "Selection-frontier closure and remaining declaration", "pdf_page": 179, "quote": "The open-selection set accordingly drops to G7 motivation and SEL-27, and SEL-27 is a theorem awaiting a PI ruling rather than a research gap — the live selection frontier is one item." }, "caution": null, "candidate_ids": [ "C2-122" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-031" }, { "type": "related_to", "target": "LIB2-032" }, { "type": "related_to", "target": "LIB2-033" }, { "type": "related_to", "target": "LIB2-316" } ], "url": "/library-v2/LIB2-324/", "content_sha256": "a6ebdba65a13aea9cfe625a22187f6c27196d78ac07e17770ff3a3d56ea238e2", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-325", "entry_version": 7, "class": "NOT_AN_ENTRY", "title": "The basepoint subgroup symbol is a typed placeholder", "statement": null, "scope": { "carrier": null, "domain": "The notation recording the type of missing basepoint datum, not a constructed or chosen subgroup.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix T", "section": "§15.5, Intrinsic-basepoint placeholder", "pdf_page": 335, "quote": "No subgroup is selected by this placeholder; without one, the transported point remains declared rather than intrinsically derived." }, "caution": null, "candidate_ids": [ "C2-132" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-005" }, { "type": "related_to", "target": "LIB2-178" } ], "url": "/library-v2/LIB2-325/", "content_sha256": "2115ea718bc3e40defa27ed26966efa61d58ae37ce91b739939cabce4cce870e", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-326", "entry_version": 7, "class": "NOT_AN_ENTRY", "title": "Source inventory and resolver tools are provenance metadata", "statement": null, "scope": { "carrier": null, "domain": "The Track-2 source-package inventory, comparator sidecars and artifact-resolver apparatus.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix X", "section": "Source-ledger and release-artifact note", "pdf_page": 343, "quote": "Every printed comparator in this suite resolves to one row of the source ledger shipped in the release bundle, not em- bedded in this PDF: ledgers/SOURCE_LEDGER_REV32.csv" }, "caution": null, "candidate_ids": [ "C2-136" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-326/", "content_sha256": "1cc777f9ed8c5b1271782232ca22ea254821d22698ceb05525157660e603edd1", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-327", "entry_version": 6, "class": "NOT_AN_ENTRY", "title": "The assumption-stack heading is programme-reference metadata", "statement": null, "scope": { "carrier": null, "domain": "The house assumption-hierarchy reference header without its original body.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": null, "caution": null, "candidate_ids": [ "C2-141" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-327/", "content_sha256": "d34f58e2403f325c5e8f3681b04b363f135abb8842ec5f7d5eaa144ffa8f1327", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-328", "entry_version": 6, "class": "NOT_AN_ENTRY", "title": "Source hold on the integral cubic coordinate map", "statement": null, "scope": { "carrier": null, "domain": "The integral cubic-preserving coordinate map named by the imported Track-2 interface record.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": null, "caution": "The source hold does not refute the proposed map or the Jordan cubic.", "candidate_ids": [ "C2-030" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-328/", "content_sha256": "f9edb0d4f3c15ec39259e3fb9c4d7908c442ce91054fdd4ab04c98b5a7e88d8c", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-329", "entry_version": 6, "class": "NOT_AN_ENTRY", "title": "Source hold on the Peirce–compact chirality-plane obstruction", "statement": null, "scope": { "carrier": null, "domain": "The specific obstruction to identifying the Peirce and compact chirality-plane triples by one cubic-preserving automorphism.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": null, "caution": "An unlocated obstruction is not a demonstrated impossibility or a refutation of the compared interfaces.", "candidate_ids": [ "C2-030" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-329/", "content_sha256": "f9e13233bfd9eb51c5743c7f69302bd76fca97de1bbc354c142885b6d05b8e16", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-330", "entry_version": 6, "class": "NOT_AN_ENTRY", "title": "Source hold on the Cayley-plus-triality frame conversion", "statement": null, "scope": { "carrier": null, "domain": "The rigid-to-local Cartan conversion into the self-dual four-form chart named in the Track-2 manifest.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": null, "caution": "No failure of the proposed frame conversion or of the registered exceptional substrate is inferred.", "candidate_ids": [ "C2-031" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-006" }, { "type": "related_to", "target": "LIB2-197" } ], "url": "/library-v2/LIB2-330/", "content_sha256": "abb3c0852bdea69dba4285bf481f8a25d6111e99f9a67294190b320ba45b1275", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-331", "entry_version": 7, "class": "NOT_AN_ENTRY", "title": "Source hold on the primitive integral Lagrangian halves", "statement": null, "scope": { "carrier": null, "domain": "The primitive integral halves of the symplectic carrier, distinct from its real Lagrangian slice.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix X", "section": "P0-1 audit, The result: real maximal isotropy", "pdf_page": 369, "quote": "LJ is a Lagrangian subspace — maximal isotropic as an identity, not by a dimension count." }, "caution": "The real Lagrangian statement neither proves nor disproves the proposed integral primitivity.", "candidate_ids": [ "C2-034" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-011" } ], "url": "/library-v2/LIB2-331/", "content_sha256": "4b9fb49de89bc9dd8ff3d80c222a022fbeac716fb0e4bd60c843f77b59bbe3b7", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-332", "entry_version": 6, "class": "NOT_AN_ENTRY", "title": "Source hold on the grading-homogeneous magnetic section", "statement": null, "scope": { "carrier": null, "domain": "The uniqueness of the magnetic section in the named grading, not the existence of a real Lagrangian boundary.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": null, "caution": "This is a source-availability hold, not a counterexample to section existence or uniqueness.", "candidate_ids": [ "C2-034" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-011" } ], "url": "/library-v2/LIB2-332/", "content_sha256": "a047109ba4bcf00cadc41e82f7d36dbb74277cc5464113b98d68b07b35b42de1", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-333", "entry_version": 7, "class": "NOT_AN_ENTRY", "title": "Source hold on the Roman–clock finite-inventory comparison", "statement": null, "scope": { "carrier": null, "domain": "The precise count-preserving comparison of Roman singular data with the occupation-clock inventory.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 1", "section": "§3, Roman singular data, not the cross-inventory theorem", "pdf_page": 26, "quote": "Under T , this locus maps to the three self-intersection double-line axes of the Roman surface." }, "caution": "Unlocated cross-inventory wording is neither a global functor no-go nor a denial of the separately printed inventories.", "candidate_ids": [ "C2-112" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-333/", "content_sha256": "4bdf997898c36a518877ea679b4eae00453ea9e3b3ff6671303cbe19650eb321", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-334", "entry_version": 6, "class": "NOT_AN_ENTRY", "title": "Roman–clock orientation-parity interface remains a proposal", "statement": null, "scope": { "carrier": null, "domain": "The proposed interface between the Roman antipodal action and the occupation clock's orientation parity.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 1", "section": "§3, Antipodal correspondence and missing spinor-bundle map", "pdf_page": 26, "quote": "no spinor-bundle map realizing the correspondence is constructed (the explicit Möbius spinor bundle for the Peirce blocks remains [OPEN] below)." }, "caution": "Two parity descriptions do not supply an equivariant map, free deck action, quotient or spinor bundle.", "candidate_ids": [ "C2-124" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-333" } ], "url": "/library-v2/LIB2-334/", "content_sha256": "8e439a537717a1877231514b199f8f3fe3c6a149556d6c7c5052e6784e2174a5", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-335", "entry_version": 7, "class": "NOT_AN_ENTRY", "title": "Source hold on the two distinct Hessian-trace quantities", "statement": null, "scope": { "carrier": null, "domain": "The house header comparing a one-loop spectral trace with a Hessian squared trace in its original parametrization.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix I", "section": "§6, Hadronic scope fence: legacy parametrization", "pdf_page": 220, "quote": "The numerical values once attached to this sector — the spectral trace A = 144, the ambient Morse index 17/27, and the baryon/meson ratio MB /MM ≈ 6.7 — were computed in the legacy ambient-27 Hessian parametrization and predate the current {ϕ, 1, ϕ−1 }/OP 2 description." }, "caution": "The missing full comparison is not a finding that either historical trace was arithmetically wrong.", "candidate_ids": [ "C2-138" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-246" } ], "url": "/library-v2/LIB2-335/", "content_sha256": "0d52554aa010e76bc68a24f4b49838751ca100eafaebf04b0fbc246eeba8a371", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-336", "entry_version": 7, "class": "NOT_AN_ENTRY", "title": "Source-equivalence hold on the AX2-elimination header", "statement": null, "scope": { "carrier": null, "domain": "The old house AX2-elimination claim and its unresolved correspondence with the current conditional selectors.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix E", "section": "§3, Remark 2: conditional role of DET-7", "pdf_page": 171, "quote": "DET-7 enters this appendix as a structural postulate, not a derived necessity; the result is therefore a conditional selector theorem." }, "caution": "No unconditional vacuum selection follows from the old elimination title or from a conditional replacement theorem.", "candidate_ids": [ "C2-139" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-018" }, { "type": "related_to", "target": "LIB2-019" }, { "type": "related_to", "target": "LIB2-020" } ], "url": "/library-v2/LIB2-336/", "content_sha256": "30ae1d48852f3ef5b0e9dfb64238143678dc79c1ba6fccc46dcc7525453a041d", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-337", "entry_version": 7, "class": "NOT_AN_ENTRY", "title": "Source-equivalence hold on the Jordan-boundary selector header", "statement": null, "scope": { "carrier": null, "domain": "The house Jordan-boundary theorem header and its unverified relation to the suite's selector statements.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix A", "section": "§A.2, Theorem 0.1: modular/Jordan-boundary sentence", "pdf_page": 141, "quote": "Equivalently, the working vacuum is the unique algebraic attractor of the present modular/Jordan-boundary construction." }, "caution": "Neither a shared vacuum target nor similar theorem wording establishes equivalence of the original assumptions.", "candidate_ids": [ "C2-140" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-019" }, { "type": "related_to", "target": "LIB2-020" } ], "url": "/library-v2/LIB2-337/", "content_sha256": "18a6b3a79addd219c9f8b9ff78a639baf37967ea620fc048da1660da8edf38f9", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-338", "entry_version": 7, "class": "NOT_AN_ENTRY", "title": "Source hold on the forced AdS base-manifold seed", "statement": null, "scope": { "carrier": null, "domain": "The house claim that the monad algebra forces the AdS base-manifold skeleton.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix T", "section": "§4, Remark 4.2: priced AdS branch", "pdf_page": 319, "quote": "The so(3, 2) reading is a conditional import of the banked sp(4, R) ∼ = so(3, 2) seed (no new fit). Absent the import, dS-vs-AdS is one discrete branch, priced." }, "caution": "An AdS algebraic seed does not by itself select a physical spacetime or establish Einstein dynamics.", "candidate_ids": [ "C2-143" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-167" }, { "type": "related_to", "target": "LIB2-168" } ], "url": "/library-v2/LIB2-338/", "content_sha256": "d753cae69a73759dbaea47f1060f8447949de4f13c066d8269b5130037fea677", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-339", "entry_version": 6, "class": "NOT_AN_ENTRY", "title": "Source hold on the CKM channel CP decomposition", "statement": null, "scope": { "carrier": null, "domain": "The named CKM CP decomposition under muon–tau symmetry in the house D140 record.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": null, "caution": "The missing decomposition statement is not a failure of either the CKM construction or the separate PMNS phase relation.", "candidate_ids": [ "C2-145" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-339/", "content_sha256": "0d1cf006431553faa493a6d4bd43ff580bd430e6c7a88f630ef094aaf7839613", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-340", "entry_version": 6, "class": "NOT_AN_ENTRY", "title": "Source hold on the CKM mixed-parity statement", "statement": null, "scope": { "carrier": null, "domain": "The house CKM channel mixed-parity claim, distinct from other parity results in the suite.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": null, "caution": "This hold does not refute mixed parity or identify it with a spin structure, octant selector or other parity theorem.", "candidate_ids": [ "C2-146" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-340/", "content_sha256": "fc083bc5b8de4c31464cee94abdaa8fbafb1955ac6bff0a36f065b2a73064942", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-341", "entry_version": 6, "class": "NOT_AN_ENTRY", "title": "Source hold on the universal mass-cascade assertion", "statement": null, "scope": { "carrier": null, "domain": "The universal physical mass-ratio interpretation of the house cascade formula, not the separately printed resolvent family.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": null, "caution": "The exact resolvent expression is not by itself a universal physical mass-ratio theorem or evidence that this house proposal was refuted.", "candidate_ids": [ "C2-148" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-341/", "content_sha256": "8cb354328ad47bf32a4429e94b8f160c194bb885f788100cf7d55ec607a886f0", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-342", "entry_version": 7, "class": "NOT_AN_ENTRY", "title": "Charge/gauge provenance terminal is a source-backed overview", "statement": null, "scope": { "carrier": null, "domain": "The programme-level charge/gauge terminal summary, with its individual constructions and obstructions separately recorded.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 0", "section": "Abstract continuation: charge/gauge terminal", "pdf_page": 2, "quote": "the charge/gauge provenance program has reached a settled terminal — possible-not-necessary, i.e. constructible but not forced —" }, "caution": "The overview is not a derivation of the gauge group or an additional independent proof of its component results.", "candidate_ids": [ "C2-149" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-076" }, { "type": "related_to", "target": "LIB2-077" }, { "type": "related_to", "target": "LIB2-081" } ], "url": "/library-v2/LIB2-342/", "content_sha256": "9e11b0862ef00514220e17b608660b06348dad4bc329655e01fca2de5762a5a1", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-343", "entry_version": 7, "class": "NOT_AN_ENTRY", "title": "Source hold on the house electroweak-loop scale", "statement": null, "scope": { "carrier": null, "domain": "The house electroweak-loop correction and its named scale, distinct from the current unresolved weak-angle matching task.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 4", "section": "§7, Undetermined matching scale", "pdf_page": 77, "quote": "as a running value the matching scale µ⋆ is scheme-dependent and undetermined" }, "caution": "The current matching task does not verify the old scale, invalidate its arithmetic or supply a completed electroweak correction.", "candidate_ids": [ "C2-155" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-199" }, { "type": "related_to", "target": "LIB2-310" } ], "url": "/library-v2/LIB2-343/", "content_sha256": "982b240a480a5dbf92ee804489f29db548010d88d85e92f1d796a3cf3f042162", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-344", "entry_version": 10, "class": "CLAIM", "title": "The generation-count forcing skeleton remains conditional", "statement": "At the printed forcing-skeleton tier, Ng = 3 is conditional on least-action selection and a smooth, ergodically mixing four-dimensional Lorentzian continuum; the engine still uses the generation count as input.", "scope": { "carrier": "The boundary-monodromy forcing skeleton", "domain": "The printed emergence/minimality argument, not a construction of replicated matter families.", "group": null, "hypotheses": [ "Require an ergodically mixing four-dimensional Lorentzian continuum.", "Require the least-action selection and smooth-continuum limit stated for minimality." ], "physical_target": null, "quantifier": "The source's conditional forcing skeleton and its stated premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 335 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "registry", "availability": "shipped" }, { "kind": "computational", "availability": "unknown" } ], "primary_source": { "component": "Appendix X", "section": "Conditional generation-count update, s496/s498", "pdf_page": 356, "quote": "Requiring an ergodically-mixing four-dimensional Lorentzian continuum to emerge forces the boundary monodromy to be hyperbolic," }, "caution": "This does not construct three gauge-identical matter families or prove the assumed continuum limit.", "candidate_ids": [ "C2-157" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-108" }, { "type": "related_to", "target": "LIB2-298" } ], "url": "/library-v2/LIB2-344/", "content_sha256": "d46e9569a6443310c0f963b582c47ba17f00aeb0ad85c56f2d7b1e6b814e9dd8", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-345", "entry_version": 7, "class": "RETIRED", "title": "Superseded use of the first JUNO oscillation comparison", "statement": "The earlier house neutrino-comparison record used the first JUNO oscillation result as its benchmark.", "scope": { "carrier": null, "domain": "The former house benchmark's operative role, not the validity of the experimental result.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "RETIRED", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 5", "section": "§1, Current comparison basis", "pdf_page": 83, "quote": "The paper therefore keeps the structure simple: the angle set, the phase formula, the current comparison to NuFIT 6.1, and the DUNE-era test scenario." }, "caution": "Superseding a comparator's operative use does not refute the experimental measurement.", "candidate_ids": [ "C2-161" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-345/", "content_sha256": "1d81eb4b6134ff3e727658b2a7017029bb4a3766c157ea605a8e06f2dadfe2c6", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-346", "entry_version": 6, "class": "NOT_AN_ENTRY", "title": "Source hold on the Gate-B matter-functor construction", "statement": null, "scope": { "carrier": null, "domain": "The combined complex-Jordan-corner and positive-kinetic-metric construction named in the repaired house heading.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": null, "caution": "The loaded one-generation dictionary and finite positive measure do not by themselves establish this different matter functor.", "candidate_ids": [ "C2-162" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-108" }, { "type": "related_to", "target": "LIB2-170" } ], "url": "/library-v2/LIB2-346/", "content_sha256": "a854181cb2d6c78e8c5f1fd2393aaa86ccf13cafd6021f492a514d1fc599b58c", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-347", "entry_version": 6, "class": "NOT_AN_ENTRY", "title": "Source hold on the meson binding-ratio formula", "statement": null, "scope": { "carrier": null, "domain": "The meson binding ratio asserted from the house two-particle-irreducible self-energy calculation.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": null, "caution": "Other occurrences of the same golden power do not verify this meson ratio or refute its missing calculation.", "candidate_ids": [ "C2-163" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-347/", "content_sha256": "442fc4e906dedb8ae4f4e79df58cbe1b37b860260c44c4502a8f50609ef75eed", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-348", "entry_version": 7, "class": "NOT_AN_ENTRY", "title": "Source hold on non-associativity as the source of hierarchy steepness", "statement": null, "scope": { "carrier": null, "domain": "The house structural interpretation of the quark–lepton hierarchy difference.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix A", "section": "§A.7.7, Remark 0.13: distinct lepton/quark duality", "pdf_page": 152, "quote": "The duality is an exact algebraic consequence of the Roman surface parametrisation and is not imposed by hand." }, "caution": "A Roman-surface hierarchy inversion is not automatically a proof of non-associativity as the cause of physical hierarchy steepness.", "candidate_ids": [ "C2-164" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-348/", "content_sha256": "5b59965ce5210da2fe11e7b87932a234ad393cf303c0addcaf5561c75806560e", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-349", "entry_version": 7, "class": "NOT_AN_ENTRY", "title": "Source-equivalence hold on the octonionic democracy postulate", "statement": null, "scope": { "carrier": null, "domain": "The old octonionic-democracy postulate and its unresolved identification with current premise and democracy statements.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 0", "section": "§2, Current operational AX3 label", "pdf_page": 13, "quote": "AX3: Minkowski balance. The operational scheme uses the current vacuum-balance condition as part of the structural framework and not as a free fit parameter." }, "caution": "A shared democracy label does not identify this postulate with the current Reynolds coefficient result or the current AX3.", "candidate_ids": [ "C2-165" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-113" } ], "url": "/library-v2/LIB2-349/", "content_sha256": "1e0c78fca20ed02e3ca4b5226fc037a55c4b5ddec84a398d742386c9b9a3506a", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-350", "entry_version": 6, "class": "NOT_AN_ENTRY", "title": "Peirce-block anti-error heading is reference metadata", "statement": null, "scope": { "carrier": null, "domain": "The house anti-error reference heading, without a specified scientific predicate or original body.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": null, "caution": null, "candidate_ids": [ "C2-166" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-350/", "content_sha256": "4aa657d61e9e46e9c4d93d7f722185bfb4a2f2588039de5b2d29f43dc9afa448", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-351", "entry_version": 6, "class": "NOT_AN_ENTRY", "title": "Source hold on the earlier solar-angle obstruction", "statement": null, "scope": { "carrier": null, "domain": "The specific obstruction in the old solar-angle house record, not the present conditional solar readout.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": null, "caution": "The current solar-angle readout does not establish that the unspecified earlier obstruction was solved or disproved.", "candidate_ids": [ "C2-170" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-060" } ], "url": "/library-v2/LIB2-351/", "content_sha256": "072a8a9c3c3a48bc3e0e9597ffaab706433113204d3383dbfbfd24fdc07dc930", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-352", "entry_version": 7, "class": "NOT_AN_ENTRY", "title": "Source hold on the T-matrix versus propagator residue comparison", "statement": null, "scope": { "carrier": null, "domain": "The house distinction between a T-matrix residue and a propagator residue in the baryon-feedback calculation.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 8", "section": "§4, Historical hadronic source pointers", "pdf_page": 125, "quote": "Library: L-BaryonMesonRatio, L-FaddeevEvasion, L-A144, L-TMatrixResidue, L-HybridMassGap." }, "caution": "A bibliography-style pointer neither proves the residue relation nor retires it with the neighbouring historical mass ratio.", "candidate_ids": [ "C2-174" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-246" } ], "url": "/library-v2/LIB2-352/", "content_sha256": "dc8abd05c79ad79b4114abd34129c01c437b0895087aa1e550820c137df4b2f4", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-353", "entry_version": 6, "class": "NOT_AN_ENTRY", "title": "Source hold on the wall-contact operator and pairing-order map", "statement": null, "scope": { "carrier": null, "domain": "The named house wall-contact operator theorem and its pairing-order map.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": null, "caution": "A similarly named contact term or measure-parity construction does not identify the missing operator theorem.", "candidate_ids": [ "C2-176" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-353/", "content_sha256": "795e0cbbaca3293c2e35e0d8a3d3dda7a75dbce9bc518da89febf51057d9a9ff", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-354", "entry_version": 7, "class": "NOT_AN_ENTRY", "title": "Source hold on the indefinite partition-function divergence claim", "statement": null, "scope": { "carrier": null, "domain": "The house divergence assertion for the unregulated partition function and its legacy Morse-index argument.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Appendix I", "section": "§6, Hadronic scope fence: legacy parametrization", "pdf_page": 220, "quote": "The numerical values once attached to this sector — the spectral trace A = 144, the ambient Morse index 17/27, and the baryon/meson ratio MB /MM ≈ 6.7 — were computed in the legacy ambient-27 Hessian parametrization and predate the current {ϕ, 1, ϕ−1 }/OP 2 description." }, "caution": "A formal homogeneity relation does not decide convergence, and a changed parametrization alone does not refute the old integral.", "candidate_ids": [ "C2-177" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-335" } ], "url": "/library-v2/LIB2-354/", "content_sha256": "0ea543305fc8b5ef980b72f016f515da1524fe5d898e51d34e5c618b5a8ee8d7", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-355", "entry_version": 7, "class": "NOT_AN_ENTRY", "title": "The charge-clock-knot tower remains on a source hold, not retired", "statement": null, "scope": { "carrier": null, "domain": "The full charge-clock-knot operator tower named by the house consolidation, whose provenance remains on hold.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": { "component": "Paper 8", "section": "§3 note, Deliberately library-resident charge-clock tower", "pdf_page": 124, "quote": "the charge-clock tower (q0KK )2 = 1/24 = 1/(4 · 6) with the ΩQ Plücker line is marked hold at source — deep but conditional, gated on the ΩQ provenance that Appendix N, The carrier truncation is also chosen shows is still a choice." }, "caution": "The printed hold does not retire the tower, select its carrier provenance or establish its full operator construction.", "candidate_ids": [ "C2-178" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [], "url": "/library-v2/LIB2-355/", "content_sha256": "9485247ea634bdf2f9fc7466dd8f03434f83dcc2f64cf301efef92246cd57c3b", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-356", "entry_version": 11, "class": "CLAIM", "title": "The internal mismatch identity is distinct from atmospheric registration", "statement": "Under DET-7 and N(J) = 1, the internal Jordan-geometry mismatch identity is sin²θmismatch = 7/16; it does not itself select the physical atmospheric-octant registration.", "scope": { "carrier": "The working Jordan vacuum and its internal mismatch geometry", "domain": "The internal Jordan-geometry corollary, not its registration to a measured mixing angle.", "group": null, "hypotheses": [ "Use the DET-7 condition and N(J) = 1 as stated in the source." ], "physical_target": null, "quantifier": "The printed internal identity under its named premises.", "real_form": null }, "source_labels_as_printed": { "math_status": "NOT_PRINTED", "attachment": "NOT_PRINTED", "scorecard_tier_word": null, "pdf_page": 59 }, "house_tier": null, "review_state": "PUBLISHED", "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)", "evidence_status": [ { "kind": "analytic", "availability": "shipped" } ], "primary_source": { "component": "Paper 3", "section": "§5.4, Internal mismatch corollary", "pdf_page": 63, "quote": "The separate internal identity sin2 θmismatch = 7/16 remains a Jordan-geometry theorem: DET-7 + N (J) = 1 fix ⟨J, J # ⟩ = 3 and the norm product ∥J∥2 ∥J # ∥2 = 16, which eliminated AX2 (D575) and gives 7/16 as a corollary" }, "caution": "This identity does not predict the physical atmospheric octant without a separately justified readout attachment.", "candidate_ids": [ "C2-005", "C2-059" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-047" }, { "type": "related_to", "target": "LIB2-048" }, { "type": "related_to", "target": "LIB2-002" }, { "type": "related_to", "target": "LIB2-100" }, { "type": "rests_on_premise", "target": "PRM-013" }, { "type": "cited_by_section", "target": "E-C05.1.claims-used" }, { "type": "cited_by_section", "target": "E-C05.1.derivation" }, { "type": "cited_by_section", "target": "E-C05.1.prior-art" } ], "url": "/library-v2/LIB2-356/", "content_sha256": "4863b1159c0276dfab45278b33f38dc0f0ffea80f04951801a3a7f318a7a82f1", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" }, { "id": "LIB2-357", "entry_version": 6, "class": "NOT_AN_ENTRY", "title": "Unidentified additional parity-lemma proposal is not an entry", "statement": null, "scope": { "carrier": null, "domain": "The additional Track-2 parity lemma requested during the discovery pass, with no supplied statement or exact source identity.", "group": null, "hypotheses": [], "physical_target": null, "quantifier": null, "real_form": null }, "source_labels_as_printed": { "math_status": null, "attachment": null, "scorecard_tier_word": null, "pdf_page": null }, "house_tier": null, "review_state": "IN_REVIEW", "scientific_status": "NOT_AN_ENTRY", "evidence_status": [ { "kind": "registry", "availability": "shipped" } ], "primary_source": null, "caution": null, "candidate_ids": [ "C2-112", "C2-124", "C2-146" ], "basis": { "pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369" }, "relationships": [ { "type": "related_to", "target": "LIB2-084" }, { "type": "related_to", "target": "LIB2-333" }, { "type": "related_to", "target": "LIB2-334" }, { "type": "related_to", "target": "LIB2-340" } ], "url": "/library-v2/LIB2-357/", "content_sha256": "cba5e6c28ba112aa3c7e9d7a565d094196a173ba2e3d0c6e814afa8f8eaa7f3e", "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02" } ] }