[{"id": "LIB2-001", "title": "Route-B admissible-gap classification", "text": "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. · 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. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-111 · Draft id G-005", "url": "/library-v2/LIB2-001/", "source": "v2 · CLAIM · H02 · DRAFTED"}, {"id": "LIB2-002", "title": "Physical atmospheric registration of the internal 7/16 mismatch", "text": "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. · 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. · Labels as printed: NOT_PRINTED / Loaded-correspondence · Candidates: C2-005 C2-059 · Draft id G-006", "url": "/library-v2/LIB2-002/", "source": "v2 · CLAIM · H04 · DRAFTED"}, {"id": "LIB2-003", "title": "SL-25: NuFIT 6.1 lower-octant atmospheric comparator", "text": "The ledger’s NuFIT normal-hierarchy, lower-octant comparator for sin²θ₂₃ is 0.470 with asymmetric errors +0.017 and −0.014. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-203 · Draft id G-007", "url": "/library-v2/LIB2-003/", "source": "v2 · COMPARATOR · H08 · DRAFTED"}, {"id": "LIB2-004", "title": "Retired house atmospheric assertion: sin²θ₂₃ = 4/7", "text": "The house entry presented an atmospheric squared-sine value as derived; its supplied source header now flags that assertion as superseded. · Candidates: C2-169 · Draft id G-008", "url": "/library-v2/LIB2-004/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-005", "title": "Joint basepoint and microscopic observation-map construction", "text": "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? · 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. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-067 C2-088 C2-097 C2-133 · Draft id G-009", "url": "/library-v2/LIB2-005/", "source": "v2 · OPEN · H10 · DRAFTED"}, {"id": "LIB2-006", "title": "The registered symplectic exceptional substrate", "text": "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. · Caution: This carrier realization does not select a compact Standard-Model frame, a gauging or a physical observable. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-035 · Draft id G-010", "url": "/library-v2/LIB2-006/", "source": "v2 · CLAIM · H01 · DRAFTED"}, {"id": "LIB2-007", "title": "The identity-anchored complementary scalar sector", "text": "The missing 16-scalar sector is identified as the identity-anchored Jordan complement 42 ⊖ 26 inside the maximal-supergravity coset. · Caution: The complement identification is not a consistent truncation to the Jordan-visible sector and does not establish the unprinted named-projector certificate. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-036 · Draft id G-011", "url": "/library-v2/LIB2-007/", "source": "v2 · CLAIM · H01 · DRAFTED"}, {"id": "LIB2-008", "title": "The Jordan-visible scalar plane fails the Lie-triple criterion", "text": "The Jordan-visible 54-plane is not a Lie-triple system: its triple brackets have nonzero projection onto the missing-16 sector. · Caution: This is a scalar sigma-model obstruction for the named plane; vector-sector and other truncation claims do not follow. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-033 · Draft id G-012", "url": "/library-v2/LIB2-008/", "source": "v2 · CLAIM · H01 · DRAFTED"}, {"id": "LIB2-009", "title": "The complementary tangent plane closes as a Lie-triple system", "text": "The registered missing-16 tangent plane is a Lie-triple system at the basepoint of E7(7)/SU(8), as reported to machine precision. · Caution: Local Lie-triple closure does not establish the global embedded quotient or a vector-coupled physical truncation. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-033 · Draft id G-013", "url": "/library-v2/LIB2-009/", "source": "v2 · CLAIM · H01 · DRAFTED"}, {"id": "LIB2-010", "title": "The algebra generated by the complementary tangent plane", "text": "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. · Caution: This local Lie-algebra identification does not prove geodesic completeness, embedding closedness or a global quotient identification. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-033 · Draft id G-014", "url": "/library-v2/LIB2-010/", "source": "v2 · CLAIM · H01 · DRAFTED"}, {"id": "LIB2-011", "title": "The cubic Jordan slice is a Lagrangian boundary of the FTS", "text": "The slice LJ = Re− ⊕ J+2 carrying the golden ladder is a 28-dimensional Lagrangian subspace of the real FTS 56. · Caution: The symplectic form contributes kinematics, not a mass-sector Hamiltonian or dynamics selector; the conjugate-section attachment remains open. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-032 · Draft id G-015", "url": "/library-v2/LIB2-011/", "source": "v2 · CLAIM · H01 · DRAFTED"}, {"id": "LIB2-012", "title": "The Albert-to-shell polarized-cubic solder", "text": "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). · Caution: Tensor equivalence does not make the unpointed shell select the transported unit or an intrinsic basepoint. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-089 · Draft id G-016", "url": "/library-v2/LIB2-012/", "source": "v2 · CLAIM · H01 · DRAFTED"}, {"id": "LIB2-013", "title": "Local positive paired-shell polarization at the transported point", "text": "At the transported point, the trace-dual polarization gives a positive three-complex-dimensional paired-shell space up to the shell-exchange torsor. · Caution: This local polarization does not select an intrinsic unpointed structure, a torsor side or the microscopic mass/generation readout. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-089 · Draft id G-017", "url": "/library-v2/LIB2-013/", "source": "v2 · CLAIM · H01 · DRAFTED"}, {"id": "LIB2-014", "title": "The active braid carrier consists of twelve Clifford-module copies", "text": "The active carrier of the frozen braid representation 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. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-103 · Draft id G-018", "url": "/library-v2/LIB2-014/", "source": "v2 · CLAIM · H01 · DRAFTED"}, {"id": "LIB2-015", "title": "The golden braid-word square root on the frozen carrier", "text": "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. · Caution: This finite spectral construction does not attach the braid word to a physical mass, an absolute energy scale or an occupied winding level. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-104 · Draft id G-019", "url": "/library-v2/LIB2-015/", "source": "v2 · CLAIM · H01 · DRAFTED"}, {"id": "LIB2-016", "title": "The physical-vector ten and selector ten are isomorphic modules", "text": "Inside V56, the so(5,5) physical-vector ten is isomorphic to the selector ten as a Kdyn module, with Casimir 1/6. · Caution: This module isomorphism does not identify either ten with the distinct boundary-adjoint module. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-109 · Draft id G-020", "url": "/library-v2/LIB2-016/", "source": "v2 · CLAIM · H01 · DRAFTED"}, {"id": "LIB2-017", "title": "The boundary and selector tens have no equivariant linear intertwiner", "text": "The boundary-adjoint ten and selector ten are inequivalent Kdyn modules: their Casimirs are 1/4 and 1/6, respectively, and HomKdyn = 0. · Caution: The linear-intertwiner obstruction does not exclude the separately counted nonlinear or symmetry-breaking bridge classes. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-109 · Draft id G-021", "url": "/library-v2/LIB2-017/", "source": "v2 · CLAIM · H01 · DRAFTED"}, {"id": "LIB2-018", "title": "DET-7 is a structural postulate in the algebraic selector", "text": "In Appendix E's algebraic selector, det Gram(Jvac,Jvac#) = 7 is imposed as the DET-7 structural postulate, not derived as a necessity. · Caution: This postulate does not establish its own first-principles necessity or the physical attachment of the resulting invariant. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-003 · Draft id G-022", "url": "/library-v2/LIB2-018/", "source": "v2 · CLAIM · H02 · DRAFTED"}, {"id": "LIB2-019", "title": "Route A selects the positive golden spectrum under its stated hypotheses", "text": "A positive real diagonal Jvac satisfying unit determinant, inversion symmetry and DET-7 has spectrum {ϕ,1,ϕ⁻¹}, unique up to permutation. · Caution: The theorem selects a spectral orbit only; it neither derives DET-7 nor selects an ordered physical Peirce frame. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-102 · Draft id G-023", "url": "/library-v2/LIB2-019/", "source": "v2 · CLAIM · H02 · DRAFTED"}, {"id": "LIB2-020", "title": "Route B selects the positive golden-unit triple under DET-7", "text": "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. · Caution: The arithmetic hypothesis and DET-7 remain premises; this result is not a derivation of the ordered physical frame or of an action. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-102 · Draft id G-024", "url": "/library-v2/LIB2-020/", "source": "v2 · CLAIM · H02 · DRAFTED"}, {"id": "LIB2-021", "title": "The finite loaded-profile parent action has its stated stable minimum", "text": "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 positive combined Hessian for every ρ,u0,κd > 0. · Caution: This finite configuration-space closure is not a continuum Hamiltonian or an interacting pole/LSZ construction. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-105 · Draft id G-025", "url": "/library-v2/LIB2-021/", "source": "v2 · CLAIM · H02 · DRAFTED"}, {"id": "LIB2-022", "title": "The finite selector closure retains the stated boundary and coupling price", "text": "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. · Caution: This incremental price neither derives the boundary datum nor supplies a programme-wide count of physically distinguishable inputs. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-105 · Draft id G-026", "url": "/library-v2/LIB2-022/", "source": "v2 · CLAIM · H02 · DRAFTED"}, {"id": "LIB2-023", "title": "The grammar detector selects the dark ray", "text": "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. · Caution: Selecting this dark ray does not select the distinct loaded boundary source ray or the nonlinear action shape. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-105 · Draft id G-027", "url": "/library-v2/LIB2-023/", "source": "v2 · CLAIM · H02 · DRAFTED"}, {"id": "LIB2-024", "title": "The selector law and clock commutator share one structure constant", "text": "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. · Caution: The shared internal coefficient does not derive external time, an absolute frequency or a physical mass scale. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-103 · Draft id G-028", "url": "/library-v2/LIB2-024/", "source": "v2 · CLAIM · H02 · DRAFTED"}, {"id": "LIB2-025", "title": "The loaded-plane defect algebra determines the selector eigenspaces", "text": "The loaded plane PB forces the 26 ⊕ 10 interior split, and its symplectic transport defect completes a commuting joint-projector construction of all five QT eigenspaces at word degree at most 2. · Caution: This subspace construction does not select the loaded plane, the eigenvalue weights or a unique nonlinear action. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-106 · Draft id G-029", "url": "/library-v2/LIB2-025/", "source": "v2 · CLAIM · H02 · DRAFTED"}, {"id": "LIB2-026", "title": "A rank-character action represents the selector Hessian", "text": "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. · Caution: A variational representation of QT does not supply a microscopic principle selecting Fchar or its nonlinear shape. · Labels as printed: Certified / NOT_PRINTED · Candidates: C2-107 · Draft id G-030", "url": "/library-v2/LIB2-026/", "source": "v2 · CLAIM · H02 · DRAFTED"}, {"id": "LIB2-027", "title": "The declared action-completion class retains nonlinear-shape freedom", "text": "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. · Caution: This obstruction is class-relative; enlarging the class changes its moduli count, and matching a Hessian alone does not select an action. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-108 · Draft id G-031", "url": "/library-v2/LIB2-027/", "source": "v2 · CLAIM · H02 · DRAFTED"}, {"id": "LIB2-028", "title": "The action-shape principle is adopted rather than intrinsically selected", "text": "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. · Caution: Adopting these relations does not derive nature's nonlinear action or remove the separate loaded boundary datum. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-108 · Draft id G-032", "url": "/library-v2/LIB2-028/", "source": "v2 · CLAIM · H02 · DRAFTED"}, {"id": "LIB2-029", "title": "The conditional selector for occupied golden mass-ladder rungs", "text": "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. · Caution: This conditional support result does not derive its vacuum-to-projector premise, a physical mass operator or atomic-state occupation. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-068 · Draft id G-033", "url": "/library-v2/LIB2-029/", "source": "v2 · CLAIM · H02 · DRAFTED"}, {"id": "LIB2-030", "title": "Target-triviality is forced in the minimal H2 class", "text": "In the predeclared minimal H2 class, target-triviality of the action clause is forced rather than assumed. · Caution: Forced target-triviality does not select the rank or the values of the coefficient map. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-116 · Draft id G-034", "url": "/library-v2/LIB2-030/", "source": "v2 · CLAIM · H02 · DRAFTED"}, {"id": "LIB2-031", "title": "The minimal H2 rank and coefficient price are predeclared", "text": "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. · Caution: The predeclared rank and standing price do not determine numerical coefficient values. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-117 · Draft id G-035", "url": "/library-v2/LIB2-031/", "source": "v2 · CLAIM · H02 · DRAFTED"}, {"id": "LIB2-032", "title": "The frozen H2 conditions do not select the coefficient map", "text": "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. · Caution: A higher-tier Sjoint, if supplied, may still derive the coefficients; the present countermodels do not exclude it. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-118 · Draft id G-036", "url": "/library-v2/LIB2-032/", "source": "v2 · CLAIM · H02 · DRAFTED"}, {"id": "LIB2-033", "title": "The banked refined-condition inventory does not select Φdiag", "text": "No refined condition family in the current banked class and condition inventory selects Φdiag non-circularly. · Caution: This is not a universal impossibility theorem; a genuinely new, independently derived invariant or condition family can reopen it. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-121 · Draft id G-037", "url": "/library-v2/LIB2-033/", "source": "v2 · CLAIM · H02 · DRAFTED"}, {"id": "LIB2-034", "title": "Casimir-naturality excludes the adopted action-shape target", "text": "In the declared coefficient class, imposing A = f(CKdyn) excludes the nonzero Φdiag target rather than selecting it. · Caution: Casimir-naturality is an additional multiplicity-blind principle, not a consequence of ordinary equivariance. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-121 · Draft id G-038", "url": "/library-v2/LIB2-034/", "source": "v2 · CLAIM · H02 · DRAFTED"}, {"id": "LIB2-035", "title": "The banked non-degenerate stability conditions leave an interior", "text": "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. · Caution: Degenerate inequalities can encode equalities, so this result is not a universal ban on dimension-reducing inequality constraints. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-121 · Draft id G-039", "url": "/library-v2/LIB2-035/", "source": "v2 · CLAIM · H02 · DRAFTED"}, {"id": "LIB2-036", "title": "An action depending only on the registered Gram map cannot select a coset point", "text": "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. · Caution: This exclusion does not apply to parent actions that use additional full-carrier or boundary information. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-105 · Draft id G-040", "url": "/library-v2/LIB2-036/", "source": "v2 · CLAIM · H02 · DRAFTED"}, {"id": "LIB2-037", "title": "The declared frame-free invariant class has no nonzero dark response", "text": "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. · Caution: A basepointed full-carrier response exists outside this frame-free reading; its basepoint is convention-loaded. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-105 · Draft id G-041", "url": "/library-v2/LIB2-037/", "source": "v2 · CLAIM · H02 · DRAFTED"}, {"id": "LIB2-038", "title": "The transported selector consumes a source without selecting its ray", "text": "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. · Caution: This source-isotropy result does not negate the later finite conditional parent-action extension or supply an intrinsic boundary datum. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-105 · Draft id G-042", "url": "/library-v2/LIB2-038/", "source": "v2 · CLAIM · H02 · DRAFTED"}, {"id": "LIB2-039", "title": "A fixed-grade cubic/current law cannot detect both dark directions", "text": "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. · 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. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-105 · Draft id G-043", "url": "/library-v2/LIB2-039/", "source": "v2 · CLAIM · H02 · DRAFTED"}, {"id": "LIB2-040", "title": "An RB-even action cannot select the horizontal-orbit sign", "text": "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. · Caution: This symmetry obstruction requires an RB-odd ingredient somewhere; it does not itself construct or select that ingredient. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-105 · Draft id G-044", "url": "/library-v2/LIB2-040/", "source": "v2 · CLAIM · H02 · DRAFTED"}, {"id": "LIB2-041", "title": "A frame-free invariant does not select the ordered Peirce frame", "text": "A frame-free F4-invariant can at best select the spectral orbit of Jvac, not its ordered frame; the registered orbit leaves at least 24 flat directions. · Caution: Selecting an ordered frame requires a loading or symmetry-breaking tensor; this result does not exclude selection with that additional datum. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-102 · Draft id G-045", "url": "/library-v2/LIB2-041/", "source": "v2 · CLAIM · H02 · DRAFTED"}, {"id": "LIB2-042", "title": "A norm-only action leaves the regular norm-level directions flat", "text": "For a twice-differentiable norm-only action S = F(α,N(X)), stationarity at a regular norm-one point forces Hess S to vanish on ker dN, leaving at least 26 flats. · 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. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-102 · Draft id G-046", "url": "/library-v2/LIB2-042/", "source": "v2 · CLAIM · H02 · DRAFTED"}, {"id": "LIB2-043", "title": "Unshifted quadratic Kempf–Ness potentials fail the selector-rank test", "text": "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. · Caution: Central shifts on proper subgroups or departure from the declared carrier/potential class are not excluded by this bound. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-108 · Draft id G-047", "url": "/library-v2/LIB2-043/", "source": "v2 · CLAIM · H02 · DRAFTED"}, {"id": "LIB2-044", "title": "A beat-invariant potential in the declared KN class cannot isolate the dark ray", "text": "In the declared unshifted zero-level quadratic-carrier Kempf–Ness class, no beat-invariant potential isolates the selector ray [W0]. · Caution: A beat-breaking spurion, dropping the clock circle or leaving the KN family exits this declared class; none is ruled out universally. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-108 · Draft id G-048", "url": "/library-v2/LIB2-044/", "source": "v2 · CLAIM · H02 · DRAFTED"}, {"id": "LIB2-045", "title": "The braid/trace grammar cannot select the boundary source datum", "text": "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. · Caution: The grammar can select the separate dark ray; this obstruction concerns the loaded boundary datum and does not exclude external selection laws. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-105 · Draft id G-049", "url": "/library-v2/LIB2-045/", "source": "v2 · CLAIM · H02 · DRAFTED"}, {"id": "LIB2-046", "title": "The golden spectrum obeys the reciprocal-square identity", "text": "The selected golden spectrum satisfies the exact internal identity 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. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-001 · Draft id G-050", "url": "/library-v2/LIB2-046/", "source": "v2 · CLAIM · H03 · DRAFTED"}, {"id": "LIB2-047", "title": "The working golden vacuum has unit Jordan determinant", "text": "At the working vacuum Jvac = diag(ϕ,1,ϕ⁻¹), the Jordan determinant is det Jvac = 1. · Caution: Unit determinant alone does not select the golden spectrum; Appendix E uses it as a normalization hypothesis. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-002 · Draft id G-051", "url": "/library-v2/LIB2-047/", "source": "v2 · CLAIM · H03 · DRAFTED"}, {"id": "LIB2-048", "title": "The selected Jordan vacuum pair has Gram determinant seven", "text": "For the selected Jordan pair (Jvac,Jvac#), the trace-form Gram determinant is 7. · Caution: The Gram value does not derive the physical atmospheric registration and is distinct from imposing DET-7 as a selector premise. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-003 · Draft id G-052", "url": "/library-v2/LIB2-048/", "source": "v2 · CLAIM · H03 · DRAFTED"}, {"id": "LIB2-049", "title": "The octonion-dimension to Jordan-rank ratio is an internal identity", "text": "The ratio dim(Os)/rank(J3) equals 8/3 as an exact dimension ratio. · Caution: An exact dimension ratio is not by itself a physical mass exponent. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-056 · Draft id G-053", "url": "/library-v2/LIB2-049/", "source": "v2 · CLAIM · H03 · DRAFTED"}, {"id": "LIB2-050", "title": "The Peirce first-row weight factors into trace and generation normalizations", "text": "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. · Caution: The exact weight does not select the first-row route or establish a universal block-weight functor. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-062 · Draft id G-054", "url": "/library-v2/LIB2-050/", "source": "v2 · CLAIM · H03 · DRAFTED"}, {"id": "LIB2-051", "title": "The registered half-weight generator has fixed octonionic coefficient", "text": "In the registered generator Thalf = Tscalar + c Toct, the C1 weight is exactly c = 1/2. · Caution: Fixing this internal coefficient does not derive the framing choice or its identification with a measured Dirac phase. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-158 · Draft id G-055", "url": "/library-v2/LIB2-051/", "source": "v2 · CLAIM · H03 · DRAFTED"}, {"id": "LIB2-052", "title": "The fixed Peirce sector has the registered unique invariant generator", "text": "Within the registered (1,3) Peirce-sector construction of f4(4), Thalf is the unique G2(2)-invariant generator. · Caution: Sector-relative uniqueness does not select the sector itself or prove the physical phase attachment. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-158 · Draft id G-056", "url": "/library-v2/LIB2-052/", "source": "v2 · CLAIM · H03 · DRAFTED"}, {"id": "LIB2-053", "title": "Frobenius compatibility fixes the finite trace ratio", "text": "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. · Caution: The unique finite trace normalization is not an LSZ residue, a low-energy mass theorem or a derived physical export. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-044 C2-054 · Draft id G-057", "url": "/library-v2/LIB2-053/", "source": "v2 · CLAIM · H03 · DRAFTED"}, {"id": "LIB2-054", "title": "The finite tick has an additive mirror-reversing grading", "text": "The banked clock weight is an exact Z4-valued grading, additive under composition and reversed by the mirror on the full registered generator set. · Caution: This grading is not a physical momentum conjugate to a constructed compact coordinate. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-029 · Draft id G-058", "url": "/library-v2/LIB2-054/", "source": "v2 · CLAIM · H03 · DRAFTED"}, {"id": "LIB2-055", "title": "The finite carrier fails the cylinder-condition count", "text": "The banked carrier requires the invariant dimension signature (1,27,27,1), whose 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. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-025 · Draft id G-059", "url": "/library-v2/LIB2-055/", "source": "v2 · CLAIM · H03 · DRAFTED"}, {"id": "LIB2-056", "title": "The selected winding symmetry model has one scale class", "text": "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. · Caution: The count does not establish exhaustiveness of the symmetry model or determine the numerical value of the physical scale. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-028 C2-069 C2-080 · Draft id G-060", "url": "/library-v2/LIB2-056/", "source": "v2 · CLAIM · H03 · DRAFTED"}, {"id": "LIB2-057", "title": "The retained PSL class-algebra coefficients", "text": "For input classes (4A,7A), the PSL(2,7) class-algebra coefficients for output classes 7A and 7B are 14 and 0, respectively. · Caution: These coefficients neither derive the current leptonic phase nor establish a mechanism relating their value to G2. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-172 · Draft id G-061", "url": "/library-v2/LIB2-057/", "source": "v2 · CLAIM · H03 · DRAFTED"}, {"id": "LIB2-058", "title": "The cubic scaling model has a constant homogeneity derivative", "text": "For the scaling action S = c N(J) on J3(Os), the source's homogeneity relation Z(c) = c⁻⁹ Z(1) gives βc := c d(log Z(c))/dc = −9. · Caution: This bare scaling identity does not determine the running of physical masses, which the source assigns to composite correlators. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-144 · Draft id G-062", "url": "/library-v2/LIB2-058/", "source": "v2 · CLAIM · H03 · DRAFTED"}, {"id": "LIB2-059", "title": "The cubic coupling is relevant by the stated power count", "text": "The source's cubic coupling has mass dimension [c] = (6 − d)/2 and is relevant in d = 4. · Caution: Power-counting relevance does not compute physical mass running or derive a numerical confinement scale. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-151 · Draft id G-063", "url": "/library-v2/LIB2-059/", "source": "v2 · CLAIM · H03 · DRAFTED"}, {"id": "LIB2-060", "title": "The solar-angle readout is conditional on ordering and the propagation interface", "text": "Under the declared normal ordering, resolvent-ladder and propagation-interface premises, the solar-angle readout is tan θ12 = √3/ϕ². · Caution: The readout does not derive the mass ordering or the ladder-to-propagation-eigenstate interface. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-004 C2-058 · Draft id G-064", "url": "/library-v2/LIB2-060/", "source": "v2 · CLAIM · H04 · DRAFTED"}, {"id": "LIB2-061", "title": "The reactor-angle formula retains an unforced round-trip readout", "text": "The retained reactor-angle formula is sin²θ13 = sin⁴(π/8); its round-trip framing and squaring are identified but not forced from first principles. · Caution: Identifying the round-trip construction does not select its physical readout or promote the formula to a theorem. · Labels as printed: Structural / NOT_PRINTED · Candidates: C2-006 C2-060 · Draft id G-065", "url": "/library-v2/LIB2-061/", "source": "v2 · CLAIM · H04 · DRAFTED"}, {"id": "LIB2-062", "title": "The leptonic Dirac-phase readout remains conditional", "text": "The retained leptonic phase readout is δCP = −2π/√5 = −160.997° under the registered framing, normal ordering, ladder/interface premises and Dirac-neutrino benchmark. · Caution: The internal rotation theorem does not by itself identify its orbit parameter with the measured Dirac phase. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-007 C2-061 · Draft id G-066", "url": "/library-v2/LIB2-062/", "source": "v2 · CLAIM · H04 · DRAFTED"}, {"id": "LIB2-063", "title": "The framework-angle Route-B readout gives the corrected Cabibbo value", "text": "The data-selected Route-B readout |Vus| = sin θ12/√6 gives 0.225256 when the framework solar angle is used. · Caution: A derived block weight does not make the data-selected route a first-principles prediction. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-009 C2-062 · Draft id G-067", "url": "/library-v2/LIB2-063/", "source": "v2 · CLAIM · H04 · DRAFTED"}, {"id": "LIB2-064", "title": "The measured-angle Cabibbo diagnostic is a different readout object", "text": "Feeding the measured NuFIT solar angle through the same first-row formula gives the separate diagnostic value |Vus| = 0.22687. · Caution: This measured-input diagnostic is not an independent prediction and does not upgrade the selected first-row route. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-062 · Draft id G-068", "url": "/library-v2/LIB2-064/", "source": "v2 · CLAIM · H04 · DRAFTED"}, {"id": "LIB2-065", "title": "The loaded first row determines its displayed Vud magnitude", "text": "The retained first-row relation |Vud| = √(1 − |Vus|² − |Vub|²) gives the displayed value 0.97429 and inherits the first-row loading. · Caution: The unitarity-derived value inherits the route choice and is not an independent confirmation of that choice. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-008 · Draft id G-069", "url": "/library-v2/LIB2-065/", "source": "v2 · CLAIM · H04 · DRAFTED"}, {"id": "LIB2-066", "title": "The Vcb formula retains its loaded physical attachment", "text": "The retained formula |Vcb| = 1/(9√7) gives 0.041996; its physical attachment inherits the atmospheric registration and the independently unforced integer 9. · Caution: The exact formula does not select its integer or derive the physical atmospheric registration on which it depends. · Labels as printed: Structural / Loaded-correspondence · Candidates: C2-010 C2-063 · Draft id G-070", "url": "/library-v2/LIB2-066/", "source": "v2 · CLAIM · H04 · DRAFTED"}, {"id": "LIB2-067", "title": "The Vub hierarchy relation inherits the loaded Route-B chain", "text": "The retained hierarchy relation |Vub| = |Vus||Vcb|/√6 gives 0.003862 within the loaded Route-B correspondence. · Caution: The hierarchy relation does not remove the route choice or supply an independent derivation of the full CKM matrix. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-011 C2-064 · Draft id G-071", "url": "/library-v2/LIB2-067/", "source": "v2 · CLAIM · H04 · DRAFTED"}, {"id": "LIB2-068", "title": "The retained CKM-phase construction remains coincidence-class", "text": "The retained construction δCKM = arctan√(3(ϕ + 5ϕ⁻⁵)) = 68.1297° remains Coincidence-class because the first-principles selection of G7 is absent. · Caution: Agreement of this numeral with data does not derive G7 or make the circular equal-shift step a selection law. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-012 C2-013 C2-065 · Draft id G-072", "url": "/library-v2/LIB2-068/", "source": "v2 · CLAIM · H04 · DRAFTED"}, {"id": "LIB2-069", "title": "The retained CKM numeral has the printed global-phase comparison", "text": "Against the named PDG global-fit Dirac phase, the suite assigns its retained CKM-phase numeral a central-value Gaussianized distance of +1.41σ. · Caution: This comparator distance is not a profile likelihood or an independent validation of the G7 selection. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-012 C2-065 · Draft id G-073", "url": "/library-v2/LIB2-069/", "source": "v2 · CLAIM · H04 · DRAFTED"}, {"id": "LIB2-070", "title": "The retained CKM numeral has a distinct direct-angle comparison", "text": "Against the named direct unitarity-triangle angle γ, the suite assigns its retained CKM-phase numeral a central-value Gaussianized distance of +0.64σ. · Caution: This comparison does not identify γ with the Dirac phase or supply a derivation of the retained numeral. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-013 C2-065 · Draft id G-074", "url": "/library-v2/LIB2-070/", "source": "v2 · CLAIM · H04 · DRAFTED"}, {"id": "LIB2-071", "title": "CKM unitarity holds by construction in the chosen parametrisation", "text": "The CKM assembly satisfies all six unitarity relations identically because it uses the standard unitary parametrisation. · Caution: Unitarity by construction is not an independent success and does not resolve the source’s CKM-angle inconsistency. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-066 · Draft id G-075", "url": "/library-v2/LIB2-071/", "source": "v2 · CLAIM · H04 · DRAFTED"}, {"id": "LIB2-072", "title": "The two CKM beta readouts remain internally inconsistent", "text": "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°. · Caution: Neither choosing the closer external comparison nor enforcing unitarity resolves the missing |Vtd| readout. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-066 · Draft id G-076", "url": "/library-v2/LIB2-072/", "source": "v2 · CLAIM · H04 · DRAFTED"}, {"id": "LIB2-073", "title": "The first-row weight is not a universal Peirce-block functor", "text": "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. · Caution: This control does not refute the first-row factorization or supply the missing block-dependent rule. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-062 · Draft id G-077", "url": "/library-v2/LIB2-073/", "source": "v2 · CLAIM · H04 · DRAFTED"}, {"id": "LIB2-074", "title": "PMNS unitarity is exact within its standard-form construction", "text": "For the displayed standard-form PMNS matrix, U†U = I exactly by construction. · Caution: Exact unitarity is not an independent falsification target and does not derive the input angles or their physical attachments. · Labels as printed: Proved / NOT_PRINTED · Candidates: C2-066 · Draft id G-078", "url": "/library-v2/LIB2-074/", "source": "v2 · CLAIM · H04 · DRAFTED"}, {"id": "LIB2-075", "title": "The uncorrected golden argument is closer on both named CKM comparisons", "text": "The zero-correction control X = ϕ gives the printed angle 65.587°, closer than the retained G7 numeral to both named CKM comparator objects. · Caution: A closer control value is not a derived replacement phase law and does not justify another data-selected formula search. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-065 · Draft id G-079", "url": "/library-v2/LIB2-075/", "source": "v2 · CLAIM · H04 · DRAFTED"}, {"id": "LIB2-076", "title": "The enumerated compact embeddings fail the simultaneous-adjoint test", "text": "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). · Caution: This record states the finite census; it neither independently verifies the broader all-frame theorem nor excludes noncompact real forms. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-037 · Draft id G-080", "url": "/library-v2/LIB2-076/", "source": "v2 · CLAIM · H05 · DRAFTED"}, {"id": "LIB2-077", "title": "The unitary matter-colour class has no image-compatible adjoint", "text": "For the registered unitary matter-colour class, the invariant embedding-tensor space has dimension 140, and the union of its rowspaces has rank 125, excluding the su(3) adjoint. · Caution: This embedding-class result does not identify a physical colour action elsewhere or supply a derivation of the compact Standard-Model boundary. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-038 · Draft id G-081", "url": "/library-v2/LIB2-077/", "source": "v2 · CLAIM · H05 · DRAFTED"}, {"id": "LIB2-078", "title": "The frame-free real 56 has no invariant rank-one Higgs projector", "text": "The bare real 56 admits no E7(7)-invariant rank-one projector; its invariant idempotents have ranks only 0 or 56. · Caution: The obstruction does not exclude a Higgs orientation supplied by a loaded boundary or selected by additional symmetry-breaking structure. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-041 · Draft id G-082", "url": "/library-v2/LIB2-078/", "source": "v2 · CLAIM · H05 · DRAFTED"}, {"id": "LIB2-079", "title": "The scanned dyonic completion hosts a classical algebra-type shadow", "text": "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. · Caution: This algebra-type shadow is not the Standard Model charge assignment, and the source makes no quantum-stability claim. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-042 · Draft id G-083", "url": "/library-v2/LIB2-079/", "source": "v2 · CLAIM · H05 · DRAFTED"}, {"id": "LIB2-080", "title": "The shadow family cannot reproduce the registered matter multiset", "text": "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. · Caution: This failure does not remove the classical shadow algebra; it rejects its identification with the required matter-charge pattern. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-042 · Draft id G-084", "url": "/library-v2/LIB2-080/", "source": "v2 · CLAIM · H05 · DRAFTED"}, {"id": "LIB2-081", "title": "The compact-completion result is conditional and enumeration-bounded", "text": "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. · Caution: The result neither derives the input gauge group nor classifies every compact reductive group on the matter space. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-043 · Draft id G-085", "url": "/library-v2/LIB2-081/", "source": "v2 · CLAIM · H05 · DRAFTED"}, {"id": "LIB2-082", "title": "The extra compact Cartan is the B−L charge direction", "text": "For the registered completion filters, the Yukawa-neutrality and anomaly equations have a one-dimensional extra-Cartan solution space generated 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. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-043 · Draft id G-086", "url": "/library-v2/LIB2-082/", "source": "v2 · CLAIM · H05 · DRAFTED"}, {"id": "LIB2-083", "title": "The loaded local matter action has a correlated Z6 kernel", "text": "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. · Caution: The faithful local quotient does not fix the physical global structure or the allowed line operators. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-043 · Draft id G-087", "url": "/library-v2/LIB2-083/", "source": "v2 · CLAIM · H05 · DRAFTED"}, {"id": "LIB2-084", "title": "The mirror ladder reproduces an NS/R parity pattern, not a spin structure", "text": "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. · Caution: The parity pattern does not construct a spin structure, a principal Spin bundle or a lift of a frame bundle. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-027 · Draft id G-088", "url": "/library-v2/LIB2-084/", "source": "v2 · CLAIM · H05 · DRAFTED"}, {"id": "LIB2-085", "title": "The finite signatures require an internal structure or its equivalent proxy", "text": "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. · Caution: This argument does not force a fifth physical spacetime dimension; a four-dimensional model may import equivalent internal data. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-026 · Draft id G-089", "url": "/library-v2/LIB2-085/", "source": "v2 · CLAIM · H05 · DRAFTED"}, {"id": "LIB2-086", "title": "The cone Hessian is colour-blind at tree level within each Peirce sector", "text": "Within each registered Peirce sector, the octonionic colour components share a single cone-Hessian eigenvalue, so G is colour-blind at tree level. · Caution: Tree-level colour isotropy does not establish all-orders colour blindness or derive the compact colour group. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-150 · Draft id G-090", "url": "/library-v2/LIB2-086/", "source": "v2 · CLAIM · H05 · DRAFTED"}, {"id": "LIB2-087", "title": "Schur block structure does not force a zero triplet eigenvalue", "text": "Schur symmetry supplies singlet–triplet block separation and scalar action λI on each irreducible triplet block, but does not force λ = 0. · Caution: This correction neither reproduces the separate numerical zeros nor provides an all-orders protection theorem. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-114 · Draft id G-091", "url": "/library-v2/LIB2-087/", "source": "v2 · CLAIM · H05 · DRAFTED"}, {"id": "LIB2-088", "title": "Generic cross-block Yukawa loops are not yet covered by an Artin generator census", "text": "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. · Caution: Lack of established two-generator containment is not a proof that a particular loop correction is non-associative or nonzero. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-114 · Draft id G-092", "url": "/library-v2/LIB2-088/", "source": "v2 · CLAIM · H05 · DRAFTED"}, {"id": "LIB2-089", "title": "The physical-to-boundary quadratic bridge space is one-dimensional", "text": "For the registered physical/selector ten P and boundary ten B, dim HomKdyn(Sym²P,B) = 1. · Caution: The dimension count does not select a normalized physical bridge or identify the inequivalent linear modules. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-120 · Draft id G-093", "url": "/library-v2/LIB2-089/", "source": "v2 · CLAIM · H05 · DRAFTED"}, {"id": "LIB2-090", "title": "The boundary-to-physical quadratic bridge space is two-dimensional", "text": "For the registered boundary ten B and physical/selector ten P, dim HomKdyn(Sym²B,P) = 2. · Caution: The available quadratic maps do not choose a copy or derive a physical boundary-to-selector response. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-120 · Draft id G-094", "url": "/library-v2/LIB2-090/", "source": "v2 · CLAIM · H05 · DRAFTED"}, {"id": "LIB2-091", "title": "The declared invariant-connection class cannot cancel the holonomy obstruction", "text": "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. · Caution: This class-relative obstruction is not a topological no-section theorem and does not exclude a non-equivariant preserving connection. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-105 · Draft id G-095", "url": "/library-v2/LIB2-091/", "source": "v2 · CLAIM · H05 · DRAFTED"}, {"id": "LIB2-092", "title": "Near-137 golden formulas carry no selection evidence under the stated density test", "text": "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. · Caution: This density result does not derive the electromagnetic coupling or assign a global significance to arbitrary formulas. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-137 · Draft id G-096", "url": "/library-v2/LIB2-092/", "source": "v2 · CLAIM · H05 · DRAFTED"}, {"id": "LIB2-093", "title": "Golden-torus robustness does not select the coupling in the tested dissipative model", "text": "In the registered Frenkel–Kontorova/Peierls–Nabarro comparison, an energy or dissipative principle mode-locks to rationals while the golden value is the unpinned, freely sliding extreme. · Caution: The comparison does not exclude all stabilization mechanisms; it does not turn robustness into a derivation of a coupling. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-137 · Draft id G-097", "url": "/library-v2/LIB2-093/", "source": "v2 · CLAIM · H05 · DRAFTED"}, {"id": "LIB2-094", "title": "A continuous Reynolds offset does not supply the discrete rung selector", "text": "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. · Caution: The distinction does not construct the winding selector or remove the premises of the conditional occupation result. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-068 · Draft id G-098", "url": "/library-v2/LIB2-094/", "source": "v2 · CLAIM · H05 · DRAFTED"}, {"id": "LIB2-095", "title": "The registered radial vacuum-decay route supplies no scale for alpha", "text": "For the registered normalized radial potential, there is no lower vacuum to tunnel to and only the trivial Euclidean solution, with Sbounce = 0; this proposed decay route supplies no dynamical scale to pin α. · Caution: The radial result neither establishes full quantum stability nor turns classical geodesic reflection into a coupling-generating decay. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-175 · Draft id G-099", "url": "/library-v2/LIB2-095/", "source": "v2 · CLAIM · H05 · DRAFTED"}, {"id": "LIB2-096", "title": "The available compact part is too small for compact colour", "text": "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. · Caution: This real-form obstruction does not ban compact colour in other carriers or derive the choice of the physical real form. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-038 · Draft id G-100", "url": "/library-v2/LIB2-096/", "source": "v2 · CLAIM · H05 · DRAFTED"}, {"id": "LIB2-097", "title": "The tested translators do not extract a common line per clock weight", "text": "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. · Caution: The nonzero and ladder-closure gates pass; this result rejects only the tested extraction of a shared line. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-038 · Draft id G-101", "url": "/library-v2/LIB2-097/", "source": "v2 · CLAIM · H05 · DRAFTED"}, {"id": "LIB2-098", "title": "The bare Freudenthal carrier does not select the electroweak framing package", "text": "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. · Caution: The obstruction leaves the marked-carrier registration conditional; it does not forbid supplying the framing as loaded input. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-041 · Draft id G-102", "url": "/library-v2/LIB2-098/", "source": "v2 · CLAIM · H05 · DRAFTED"}, {"id": "LIB2-099", "title": "The orphan-doublet ruling is class-relative and the finite subgate is not the full row", "text": "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. · Caution: The local exclusion does not reach genuinely external categories, and a passing finite subgate is not a continuum result. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-105 · Draft id G-103", "url": "/library-v2/LIB2-099/", "source": "v2 · CLAIM · H05 · DRAFTED"}, {"id": "LIB2-100", "title": "The registered octant construction does not exclude the mirror registration", "text": "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. · Caution: The nonselection result does not refute the internal mismatch identity or derive a theory-fixed odd coupling sign. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-005 C2-059 · Draft id G-104", "url": "/library-v2/LIB2-100/", "source": "v2 · CLAIM · H05 · DRAFTED"}, {"id": "LIB2-101", "title": "The registered ladder and phase census contains no selected complex rung ratio", "text": "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. · Caution: Commuting scaling and phase candidates do not by themselves select a nonzero phase or its physical attachment. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-104 · Draft id G-105", "url": "/library-v2/LIB2-101/", "source": "v2 · CLAIM · H05 · DRAFTED"}, {"id": "LIB2-102", "title": "The registered Jordan-scaling centralizer has the printed dimension and signature", "text": "The registered scaling centralizer C(Lvac) ⊂ e6(6) has dimension 30, displayed signature (18,12,0), and centre dimension 2. · Caution: A compact subalgebra inside the centralizer does not select a complex structure, angle or physical rung-to-phase map. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-104 · Draft id G-106", "url": "/library-v2/LIB2-102/", "source": "v2 · CLAIM · H05 · DRAFTED"}, {"id": "LIB2-103", "title": "The registered grading centralizer has the printed dimension and signature", "text": "The registered grading centralizer C(H) ⊂ e7(7) has dimension 79, displayed signature (43,36,0), and centre dimension 1. · Caution: The presence of compact directions does not fix their angles, and the Appendix-H K is not a member of this centralizer. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-104 · Draft id G-107", "url": "/library-v2/LIB2-103/", "source": "v2 · CLAIM · H05 · DRAFTED"}, {"id": "LIB2-104", "title": "The bare quartic is not stationary at the registered golden boundary point", "text": "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. · Caution: Nonstationarity of the bare quartic does not contradict stationarity of a separately constrained or sourced action. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-042 · Draft id G-108", "url": "/library-v2/LIB2-104/", "source": "v2 · CLAIM · H05 · DRAFTED"}, {"id": "LIB2-105", "title": "The stated split-G2 involution family yields no positive equivariant polarization", "text": "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. · Caution: The exclusion is confined to the stated equivariant split-real involutions; it does not rule out polarizations using additional data. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-042 · Draft id G-109", "url": "/library-v2/LIB2-105/", "source": "v2 · CLAIM · H05 · DRAFTED"}, {"id": "LIB2-106", "title": "The exact single-chi additive ratio completion fails on the registered support", "text": "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. · Caution: This exact-class failure leaves the depth skeleton and approximate shape intact and is not a universal two-parameter no-go. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-055 · Draft id G-110", "url": "/library-v2/LIB2-106/", "source": "v2 · CLAIM · H05 · DRAFTED"}, {"id": "LIB2-107", "title": "The signed metric-weighted residue cannot supply the positive seven count", "text": "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. · Caution: This bound does not refute the finite trace/index theorem or exclude every non-residue physical realization of the ratio. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-044 C2-054 · Draft id G-111", "url": "/library-v2/LIB2-107/", "source": "v2 · CLAIM · H05 · DRAFTED"}, {"id": "LIB2-108", "title": "The explicit B-map fixes a loaded one-generation field dictionary", "text": "Under the explicit B-map and compact field dictionary, the one-generation quark and lepton placements and all sixteen hypercharges are fixed. · Caution: This one-generation dictionary does not select the compact gauge boundary or construct the explicit three-generation embedding. · Labels as printed: Proved / NOT_PRINTED · Candidates: C2-040 · Draft id G-112", "url": "/library-v2/LIB2-108/", "source": "v2 · CLAIM · H06 · DRAFTED"}, {"id": "LIB2-109", "title": "The loaded one-generation dictionary cancels the stated anomalies", "text": "Under the explicit B + SU(5) embedding, the one-generation Standard-Model gauge and gravitational anomaly sums vanish, and the Witten SU(2) anomaly is absent. · Caution: Anomaly cancellation does not select the compact embedding or determine the number of complete generations. · Labels as printed: Proved / NOT_PRINTED · Candidates: C2-040 · Draft id G-113", "url": "/library-v2/LIB2-109/", "source": "v2 · CLAIM · H06 · DRAFTED"}, {"id": "LIB2-110", "title": "The loaded split-octonion cubic has a nonzero invariant trilinear", "text": "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. · Caution: The existence of this invariant does not establish its uniqueness or determine physical Yukawa coefficients. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-052 · Draft id G-114", "url": "/library-v2/LIB2-110/", "source": "v2 · CLAIM · H06 · DRAFTED"}, {"id": "LIB2-111", "title": "The loaded hypercharge projection gives the four Yukawa tensors", "text": "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}. · Caution: The projected tensor structure does not select the loaded hypercharge action or split the four coefficient values. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-053 · Draft id G-115", "url": "/library-v2/LIB2-111/", "source": "v2 · CLAIM · H06 · DRAFTED"}, {"id": "LIB2-112", "title": "Exactly half of the raw trilinear norm lies in forbidden mirror sectors", "text": "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. · Caution: Removing forbidden mirror components does not derive the hypercharge loading or create a non-democratic hierarchy. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-047 · Draft id G-116", "url": "/library-v2/LIB2-112/", "source": "v2 · CLAIM · H06 · DRAFTED"}, {"id": "LIB2-113", "title": "The registered invariant coefficient channel is the democratic ray", "text": "In the registered multiplicity-one equivariant setting, Reynolds projection leaves the common Yukawa coefficient ray (1,1,1,1). · Caution: This UV coefficient ray does not predict equal low-energy masses or select a symmetry-breaking compensator. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-046 · Draft id G-117", "url": "/library-v2/LIB2-113/", "source": "v2 · CLAIM · H06 · DRAFTED"}, {"id": "LIB2-114", "title": "The registered compensator candidates do not produce the hierarchy", "text": "The banked enhanced-symmetry and compensator candidates fail to produce the target within-generation hierarchy while respecting the projected Yukawa channel census. · Caution: The finite sweep does not exclude unbanked non-perturbative, composite or other symmetry-breaking mechanisms. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-045 · Draft id G-118", "url": "/library-v2/LIB2-114/", "source": "v2 · CLAIM · H06 · DRAFTED"}, {"id": "LIB2-115", "title": "The unrestricted residue map can reproduce any positive Yukawa quartet", "text": "The registered residue-incidence map has rank 4 over eight independent Z-factors, so free field residues can realize any positive Yukawa quartet. · Caution: Reproducing a quartet through free residues does not explain it; the parent must determine the residues and thresholds. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-050 · Draft id G-119", "url": "/library-v2/LIB2-115/", "source": "v2 · CLAIM · H06 · DRAFTED"}, {"id": "LIB2-116", "title": "The displayed one-loop trajectory produces only an order-one spread", "text": "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. · Caution: This single perturbative trajectory does not exclude every threshold or non-perturbative mechanism. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-051 · Draft id G-120", "url": "/library-v2/LIB2-116/", "source": "v2 · CLAIM · H06 · DRAFTED"}, {"id": "LIB2-117", "title": "The edge-uniform parent metric has zero relative Yukawa rank", "text": "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. · Caution: The zero relative rank belongs to this parent geometry and does not exclude more general symmetry-breaking residues. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-049 · Draft id G-121", "url": "/library-v2/LIB2-117/", "source": "v2 · CLAIM · H06 · DRAFTED"}, {"id": "LIB2-118", "title": "The banked parent does not determine the within-generation hierarchy", "text": "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. · Caution: The conclusion does not exclude an unbanked parent, non-perturbative dynamics or composite strong-coupling mechanisms. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-048 · Draft id G-122", "url": "/library-v2/LIB2-118/", "source": "v2 · CLAIM · H06 · DRAFTED"}, {"id": "LIB2-119", "title": "The same-block Peirce contraction extracts the unit middle weight", "text": "In the registered same-block (1,3) Peirce carrier, the cubic invariant 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. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-016 · Draft id G-123", "url": "/library-v2/LIB2-119/", "source": "v2 · CLAIM · H06 · DRAFTED"}, {"id": "LIB2-120", "title": "W01 declares the Planck-scale top-Yukawa attachment", "text": "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. · Caution: This ultraviolet registration is not a proof of the physical coupling or its value after low-energy running and matching. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-016 · Draft id G-124", "url": "/library-v2/LIB2-120/", "source": "v2 · CLAIM · H06 · DRAFTED"}, {"id": "LIB2-121", "title": "The top tree estimate retains a status-ineligible cross-scheme offset", "text": "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. · Caution: The cross-scheme offset is not a physics tension; a scheme-matched conclusion requires the missing matching prescription. · Labels as printed: Structural / NOT_PRINTED · Candidates: C2-017 · Draft id G-125", "url": "/library-v2/LIB2-121/", "source": "v2 · CLAIM · H06 · DRAFTED"}, {"id": "LIB2-122", "title": "The muon-to-tau formula is a loaded reproduced ratio", "text": "The retained ratio mµ/mτ = (ϕ/√5)^(8/3)·√2/10 = 0.059684 is Structural mathematically, Loaded-correspondence physically and Reproduced numerically. · Caution: Exact dimension quantities do not by themselves derive their use as a mass exponent and physical normalization. · Labels as printed: Structural / Loaded-correspondence · Candidates: C2-056 · Draft id G-126", "url": "/library-v2/LIB2-122/", "source": "v2 · CLAIM · H06 · DRAFTED"}, {"id": "LIB2-123", "title": "The muon-ratio residual is the multiplicative coefficient gap", "text": "The +0.37% muon-to-tau residual is the multiplicative gap between Creq = 0.140900 and the offered C = 0.141421, not an additional correction above a completed derivation. · Caution: The separate QED matching step does not supply the missing derivation of this coefficient or erase its target-first provenance. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-056 · Draft id G-127", "url": "/library-v2/LIB2-123/", "source": "v2 · CLAIM · H06 · DRAFTED"}, {"id": "LIB2-124", "title": "The mass-formula chains retain three named dimensional anchors", "text": "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. · Caution: The abstract one-class theorem does not by itself supply the relations and uncertainties connecting these empirical anchors. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-113 · Draft id G-128", "url": "/library-v2/LIB2-124/", "source": "v2 · CLAIM · H06 · DRAFTED"}, {"id": "LIB2-125", "title": "The tau-anchored muon tree estimate inherits the loaded ratio", "text": "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. · Caution: This mass estimate inherits the target-first coefficient gap and is not independent of the measured tau anchor. · Labels as printed: Structural / Loaded-correspondence · Candidates: C2-018 · Draft id G-129", "url": "/library-v2/LIB2-125/", "source": "v2 · CLAIM · H06 · DRAFTED"}, {"id": "LIB2-126", "title": "The separate QED matching step gives the displayed physical muon mass", "text": "The stated QED matching step divides the muon tree value by 1 + δQED, with δQED = +0.3125%, giving mµ,phys = 105.72 MeV. · Caution: The QED correction does not derive the loaded coefficient or account for its separate fit gap. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-019 · Draft id G-130", "url": "/library-v2/LIB2-126/", "source": "v2 · CLAIM · H06 · DRAFTED"}, {"id": "LIB2-127", "title": "The electron value is the light Koide root under an external empirical rule", "text": "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. · Caution: This empirical-rule closure does not derive the electron mass from the bare Jordan algebra or remove the muon-chain loading. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-020 C2-057 · Draft id G-131", "url": "/library-v2/LIB2-127/", "source": "v2 · CLAIM · H06 · DRAFTED"}, {"id": "LIB2-128", "title": "The light-quark constituent proxy uses the fitted hadronic anchor", "text": "The retained light-quark constituent relation is m_u^const ≈ m_d^const ≈ ΛG2 ϕ^(1/2) ≈ 331 MeV. · Caution: This constituent proxy is not directly comparable to current-quark masses and does not derive the hadronic anchor. · Labels as printed: Structural / NOT_PRINTED · Candidates: C2-023 · Draft id G-132", "url": "/library-v2/LIB2-128/", "source": "v2 · CLAIM · H06 · DRAFTED"}, {"id": "LIB2-129", "title": "The strange constituent proxy carries the printed Casimir modifier", "text": "The source gives m_s^const = ΛG2 ϕ(KG2/KSU(3))^(1/4) = 553.7 MeV for the strange constituent proxy. · Caution: This constituent proxy does not supply a constituent-to-MS conversion or derive the hadronic scale. · Labels as printed: Structural / NOT_PRINTED · Candidates: C2-022 · Draft id G-133", "url": "/library-v2/LIB2-129/", "source": "v2 · CLAIM · H06 · DRAFTED"}, {"id": "LIB2-130", "title": "The bottom bridge retains its tau anchor and cross-scheme offset", "text": "The retained bottom bridge mb = (7/3)mτ = 4146 MeV has the printed −0.96% offset from the MS-bar comparator, a cross-scheme comparison that sets no status. · Caution: The bridge is not a derived low-energy MS-bar mass relation, and its comparator distance is not a scheme-matched tension. · Labels as printed: Structural / NOT_PRINTED · Candidates: C2-021 · Draft id G-134", "url": "/library-v2/LIB2-130/", "source": "v2 · CLAIM · H06 · DRAFTED"}, {"id": "LIB2-131", "title": "The charm bridge remains constituent-anchored and cross-scheme", "text": "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. · Caution: This constituent-anchored comparison does not establish a low-energy mass theorem or a status-setting discrepancy. · Labels as printed: Structural / NOT_PRINTED · Candidates: C2-022 · Draft id G-135", "url": "/library-v2/LIB2-131/", "source": "v2 · CLAIM · H06 · DRAFTED"}, {"id": "LIB2-132", "title": "The tested untuned running and matching readings do not remove the heavy-quark offsets", "text": "The tested untuned SM/QCD running-and-matching readings do not remove the top, bottom and charm boundary-value offsets. · Caution: The negative audit does not exclude all threshold physics or turn the cross-scheme offsets into matched statistical tensions. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-017 C2-021 C2-022 · Draft id G-136", "url": "/library-v2/LIB2-132/", "source": "v2 · CLAIM · H06 · DRAFTED"}, {"id": "LIB2-133", "title": "The outer-mirror charged-lepton fit consumes two free gaps", "text": "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. · Caution: Fitting two gaps to two ratios provides no prediction of those fitted ratios and does not reconcile the two mass routes. · Labels as printed: Input / NOT_PRINTED · Candidates: C2-056 · Draft id G-137", "url": "/library-v2/LIB2-133/", "source": "v2 · CLAIM · H06 · DRAFTED"}, {"id": "LIB2-134", "title": "The literal Jordan-adjoint neutrino mass reading fails its splitting-ratio test", "text": "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. · Caution: This failed mass interpretation does not refute the internal mixing carrier or derive an absolute neutrino mass scale. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-024 C2-126 · Draft id G-138", "url": "/library-v2/LIB2-134/", "source": "v2 · CLAIM · H06 · DRAFTED"}, {"id": "LIB2-135", "title": "The spectral-gap model imposes its self-consistency through the lifted cone trace", "text": "In the stated spectral-singularity model, T(ε) = A/ε and ε = m² = αA give αT = 1 and the scale relation Λ² = αA. · Caution: The relation does not determine a numerical confinement scale independently of its coupling and calibration inputs. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-160 · Draft id G-139", "url": "/library-v2/LIB2-135/", "source": "v2 · CLAIM · H06 · DRAFTED"}, {"id": "LIB2-136", "title": "The baryonic cubic channel is distinct from the cancelled quadratic channel", "text": "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. · Caution: The tensor distinction is not a derived baryon spectrum, a mass ratio or an independently constructed physical residue. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-156 · Draft id G-140", "url": "/library-v2/LIB2-136/", "source": "v2 · CLAIM · H06 · DRAFTED"}, {"id": "LIB2-137", "title": "The cone expansion uses a spectral background rather than stationarity of the cubic", "text": "The source organizes the cone expansion at Jvac by the Hessian spectrum rather than stationary phase of N, because ∇N ≠ 0 there. · Caution: This expansion prescription does not establish a stationary or stable vacuum of a different gauged or sourced action. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-171 · Draft id G-141", "url": "/library-v2/LIB2-137/", "source": "v2 · CLAIM · H06 · DRAFTED"}, {"id": "LIB2-138", "title": "The compact two-scale Gram class excludes its previously priced half-ratio", "text": "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. · Caution: The exclusion is not universal and does not refute the distinct finite 7/3 index or unification-ratio statement. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-110 · Draft id G-142", "url": "/library-v2/LIB2-138/", "source": "v2 · CLAIM · H06 · DRAFTED"}, {"id": "LIB2-139", "title": "The declared top-Yukawa boundary has a separately reported running value", "text": "The suite reports that RG evolution of its declared yt(MPl) = 1 boundary gives yt(MZ) ≈ 0.967 in the low-energy effective theory. · Caution: The running value inherits W01 and does not equate the two scale-dependent couplings or complete the top-mass matching. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-016 · Draft id G-143", "url": "/library-v2/LIB2-139/", "source": "v2 · CLAIM · H06 · DRAFTED"}, {"id": "LIB2-140", "title": "The selected neutrino rung is a below-floor edge target, not a mass relation", "text": "The selected rung R2 = 1/(ϕ⁴ − 1) = 0.17082, whose square is 0.02918, is retained only as a below-floor edge target under normal ordering and m1 ≲ 1 meV, not as a mass relation or a hit. · 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. · Labels as printed: Structural / NOT_PRINTED · Candidates: C2-127 · Draft id G-144", "url": "/library-v2/LIB2-140/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-141", "title": "The neutrino depth assignment is post-hoc and receives no blind credit", "text": "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. · Caution: This post-hoc rule is not a theory-selected assignment, and its fit preference does not supply a physical neutrino mass operator. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-127 · Draft id G-145", "url": "/library-v2/LIB2-141/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-142", "title": "The lightest-mass boundary has mass-sum and beta-decay corollaries", "text": "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. · Caution: These boundary values do not derive the R2 attachment, an absolute neutrino mass scale from the algebra, or a cosmological exclusion. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-127 · Draft id G-146", "url": "/library-v2/LIB2-142/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-143", "title": "The exhibited winding-to-Fibonacci functor defines the finite cluster image", "text": "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. · Caution: The finite functor does not construct a continuum Yang–Mills functor or convert a categorical weight into an energy without the declared interface. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-073 · Draft id G-147", "url": "/library-v2/LIB2-143/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-144", "title": "The cluster-ledger interface is the declared weight-to-energy map", "text": "The categorical construction fixes the ledger weights Tn; the declared cluster-ledger interface carries them, together with the alpha-cell and triple-alpha terms, to dimensionless nuclear binding energies. · Caution: The interface does not derive the absolute energy unit or make the categorical associativity identity itself an energy. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-073 C2-077 · Draft id G-148", "url": "/library-v2/LIB2-144/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-145", "title": "The small-nucleus kernel is triangularly saturated", "text": "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. · Caution: The initial fit does not independently predict the nuclei used to fix its coefficients or establish the later continuations. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-076 · Draft id G-149", "url": "/library-v2/LIB2-145/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-146", "title": "The closed alpha-cell typing gives the A = 5 gap", "text": "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. · Caution: The gap depends on the registered cell typing and does not determine the full charge-magnitude sector. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-074 · Draft id G-150", "url": "/library-v2/LIB2-146/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-147", "title": "The two-alpha typing gives a negative first correction at A = 8", "text": "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. · Caution: This channel result does not give a complete nuclear Hamiltonian or settle the separate charge and breathing-accounting problems. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-074 · Draft id G-151", "url": "/library-v2/LIB2-147/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-148", "title": "The composition ladder is a finite trace invariant", "text": "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. · Caution: The finite trace law does not on its own derive a binding energy or a continuum Yang–Mills functor. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-077 · Draft id G-152", "url": "/library-v2/LIB2-148/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-149", "title": "The residual-circulation weights obey the printed piecewise rule", "text": "The registered residual trace weights are ε5 = −ϕ⁻², ε6 = 0 and εn = ϕ^(5−n) for n ≥ 7. · Caution: The piecewise weight rule does not by itself define a physical energy correction or justify an untyped change to a binding formula. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-077 · Draft id G-153", "url": "/library-v2/LIB2-149/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-150", "title": "The suite reports a sealed pentagon-weight match", "text": "The suite reports that the derived pentagon weight T5 = ϕ² = 2.618034 matched the sealed implied value 2.617965 at 26 ppm. · Caution: The reported vault match is not a new blind receipt, a global statistical significance or a derivation of the energy interface. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-077 · Draft id G-154", "url": "/library-v2/LIB2-150/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-151", "title": "The suite reports a sealed ninth-weight match", "text": "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. · Caution: This reported match does not establish a universal forecast rate or certify a new blind result in the library-drafting round. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-077 · Draft id G-155", "url": "/library-v2/LIB2-151/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-152", "title": "The Hoyle excitation passes the source's frozen bar", "text": "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. · Caution: The source-reported pass does not turn the associator into an energy or derive the dimensional scale and full nuclear dynamics. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-075 · Draft id G-156", "url": "/library-v2/LIB2-152/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-153", "title": "The freeze-state ledger records sharp passes and a separately typed obstruction", "text": "The freeze-state ledger reports seventeen sharp binding-energy passes from deuterium through calcium plus one typed silicon obstruction, with 0.37% labelled as its worst untyped residual. · Caution: The aggregate report is not an independent re-audit, a global likelihood or a completed charge-magnitude and shell model. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-078 · Draft id G-157", "url": "/library-v2/LIB2-153/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-154", "title": "The silicon residual passed its original bar and took the typed-obstruction branch", "text": "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. · Caution: This disposition neither proves universal irreducibility nor resolves the separate silicon readout fork or packing mechanism. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-083 · Draft id G-158", "url": "/library-v2/LIB2-154/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-155", "title": "The charge-magnitude ledger retains two exposed proton-separation defects", "text": "Under the banked baseline ruling, the proton-separation estimates Sp(9B) and Sp(8B) are respectively 1.29 and 2.60 times the world values; correct signs and counts do not close the magnitude sector. · Caution: The strong sign/count record does not derive charge magnitudes or justify choosing a more favourable baseline after comparison. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-072 · Draft id G-159", "url": "/library-v2/LIB2-155/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-156", "title": "The direct Markov-second-moment repair has the wrong sign", "text": "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. · Caution: This excludes the declared direct attachment, not every annular operator or an independently derived negative energy map. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-083 C2-128 · Draft id G-160", "url": "/library-v2/LIB2-156/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-157", "title": "The connected second moment does not switch off at the later cells", "text": "The ribbon full-twist identity leaves the registered connected Markov second moment strictly positive at n = 8,9,10, excluding exact switch-off there. · Caution: Nonzero later moments do not settle the finite support-threshold test, whose energy coefficient remains open. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-083 C2-128 · Draft id G-161", "url": "/library-v2/LIB2-157/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-158", "title": "The tested perturbative annular attachment does not explain the deficit window", "text": "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. · Caution: The tested annular failures do not exclude the separately named packing/coordination class or constitute a universal annular no-go. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-083 C2-128 · Draft id G-162", "url": "/library-v2/LIB2-158/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-159", "title": "The separate silicon readout remains a three-way fork", "text": "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. · Caution: No branch is selected, and this fork is not the separately scored first-circulation binding residual. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-083 · Draft id G-163", "url": "/library-v2/LIB2-159/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-160", "title": "The fixed-Z isospin coefficient is selected rather than derived", "text": "The isospin Casimir coefficient χ = ϕ⁻⁶T3 is selected on the fixed-Z chains, not derived; the source carries the sector as loaded. · Caution: The selected coefficient is not a derived isospin magnitude law or a prediction of the neutron–proton mass difference. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-129 · Draft id G-164", "url": "/library-v2/LIB2-160/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-161", "title": "The registered up–down operation is a parity, not a derived isospin action", "text": "The registered u ↔ d operation is the split-octonion conjugation e7 → −e7, exchanging Hu and Hd as a Z2 parity rather than a derived SU(2) action. · Caution: The parity does not construct a continuous isospin action or supply the missing QCD flip energy. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-129 · Draft id G-165", "url": "/library-v2/LIB2-161/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-162", "title": "The registered breathing weight is mirror-even and charge-blind", "text": "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. · Caution: The weight does not determine whether the excitation occurs in every parent typing; the A = 8 accounting remains open. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-073 C2-075 · Draft id G-166", "url": "/library-v2/LIB2-162/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-163", "title": "The separation-energy rule uses the refined daughter ledger", "text": "The banked separation-energy rule is Sx(P → D + x) = B(P) − B(Dledger), with the refined daughter always; neutral excitations cancel only when present in both typings. · Caution: The convention does not supply the missing parent-excitation typing or resolve the exposed charge-magnitude defects. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-072 · Draft id G-167", "url": "/library-v2/LIB2-163/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-164", "title": "The draft glueball pair falls in the two printed frozen bands", "text": "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]. · Caution: The band matches are draft-tier source reports, not a continuum Yang–Mills construction or an absolute glueball-scale derivation. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-078 C2-099 · Draft id G-168", "url": "/library-v2/LIB2-164/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-165", "title": "The finite Gaussian OS subgate is reported as a conditional checkpoint", "text": "The source reports a finite Gaussian Osterwalder–Schrader subgate pass at conditional/finite tier, not a reflection-positive continuum construction. · Caution: The finite subgate does not establish a continuum limit, a reflection-positive continuum measure, an interacting pole or LSZ. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-119 · Draft id G-169", "url": "/library-v2/LIB2-165/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-166", "title": "The toy resolvent remains a finite conditional checkpoint", "text": "The toy resolvent accompanying the Gaussian subgate is source-reported as two-host byte-certified at conditional/finite tier. · Caution: The toy resolvent does not constitute an interacting physical propagator, a pole theorem or an LSZ construction. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-119 · Draft id G-170", "url": "/library-v2/LIB2-166/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-167", "title": "The motivated clock seed is extra structure, not an energy order of tensor layers", "text": "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. · Caution: The motivated seed does not derive measured time, a physical energy ordering, masses or the missing continuum functor. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-123 C2-154 · Draft id G-171", "url": "/library-v2/LIB2-167/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-168", "title": "The trace-built MacDowell–Mansouri action is a signature-sector candidate", "text": "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. · Caution: This candidate is not the full particle, generation, gauge or mass action and does not restore the rejected parent-action route. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-091 · Draft id G-172", "url": "/library-v2/LIB2-168/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-169", "title": "The Euclidean MM/EH action has the stated conformal instability", "text": "The Euclidean MacDowell–Mansouri/Einstein–Hilbert action is unbounded below in the conformal direction in the registered convention. · Caution: This sign obstruction does not exclude regulated positive measures or a constrained completion outside the pure weight. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-086 · Draft id G-173", "url": "/library-v2/LIB2-169/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-170", "title": "A reflection-positive Cartan state exists at finite regulator", "text": "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. · Caution: Finite-regulator existence does not establish the continuum limit, Einstein universality or a selected coherent boundary state. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-094 · Draft id G-174", "url": "/library-v2/LIB2-170/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-171", "title": "The pure MacDowell–Mansouri quadratic form is not a positive covariance", "text": "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. · Caution: This finite-algebraic obstruction does not exclude the positive completion family or prove that a finite Cartan state is Einstein gravity. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-095 · Draft id G-175", "url": "/library-v2/LIB2-171/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-172", "title": "The positive completion cone has a strict coefficient domain", "text": "The registered quadratic completion Bα,β = αBC + βBMM is positive definite exactly when α > 0 and |β| < α; its boundary α = |β| is chiral-null. · Caution: Positive quadratic completion does not establish Einstein universality, a continuum limit or generic nonlinear reflection positivity. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-095 · Draft id G-176", "url": "/library-v2/LIB2-172/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-173", "title": "The ordered state pair supplies the additive relative modular score", "text": "For the registered ordered golden state pair, the additive half-log score is Krel = Dϕ = diag(1,0,−1) on the golden lattice. · Caution: The score does not intrinsically select the ordered state pair or construct the microscopic mass/generation readout. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-093 · Draft id G-177", "url": "/library-v2/LIB2-173/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-174", "title": "The record-quotient observation composite is unique under its seven premises", "text": "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. · Caution: This construction does not select a microscopic realization, restore excluded support or build the distinct mass/generation observation map. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-093 · Draft id G-178", "url": "/library-v2/LIB2-174/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-175", "title": "The supported MOS quotient has rank three and relative rank two", "text": "The supported observation quotient ΠMOS has rank 3 and relative rank 2 < 5; it is not the full microscopic loading. · Caution: The finite quotient does not restore missing microscopic modes or discharge the full observation-map construction. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-092 · Draft id G-179", "url": "/library-v2/LIB2-175/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-176", "title": "History, character and boundary record are one registered record type", "text": "In the OMOS record process, history, character and boundary record describe one object: branch norms equal cylinder probabilities and distinct histories are orthogonal. · Caution: The equivalence of record descriptions does not determine which particular history is realized. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-085 · Draft id G-180", "url": "/library-v2/LIB2-176/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-177", "title": "The realized history is sample data rather than a value selected by its law", "text": "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. · Caution: This typing does not predict the specific realized outcome or remove the source's separate conserved-sector and history-candidate conditions. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-085 · Draft id G-181", "url": "/library-v2/LIB2-177/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-178", "title": "The locked basepoint census has no qualifying intrinsic datum", "text": "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. · 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. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-133 · Draft id G-182", "url": "/library-v2/LIB2-178/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-179", "title": "The registered stabilizer has no nonzero invariant odd covector", "text": "The largest registered stabilizer subgroup preserving J− has no nonzero invariant covector on J−, blocking the attempted invariant scalar row. · Caution: The invariant-row obstruction does not exclude a state-dependent covariant response or determine its physical normalization. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-134 · Draft id G-183", "url": "/library-v2/LIB2-179/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-180", "title": "The transported A689 grading has trivial rather than alternating character", "text": "The transported A689 split-norm Z2 grading carries the trivial, not alternating, S3 character, so its direct identification with Hsgn is closed negative. · Caution: This character mismatch does not eliminate covariant source-character intertwiners or select an endpoint orientation. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-134 · Draft id G-184", "url": "/library-v2/LIB2-180/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-181", "title": "The local covariant odd response is one orbit with an unselected torsor", "text": "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. · Caution: A single equivalence class is not a selected representative, endpoint orientation or physical response coefficient. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-134 · Draft id G-185", "url": "/library-v2/LIB2-181/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-182", "title": "The MOS channel family permits a range of odd-response amplitudes", "text": "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. · Caution: Complete positivity and whitening do not select the endpoint or provide a microscopic support-restoring observation map. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-135 · Draft id G-186", "url": "/library-v2/LIB2-182/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-183", "title": "The reversal-covariant score solder bounds the product response", "text": "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. · Caution: The product bound does not force a unit response or close the distinct microscopic observation and normalization problems. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-135 · Draft id G-187", "url": "/library-v2/LIB2-183/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-184", "title": "The registered normalization census contains no forcing row", "text": "The complete registered normalization census grew from 28 to 40 typed rows with zero forcing rows; none of the banked conditions fixes |λµ|. · Caution: The census does not exclude a new microscopic support-restoring map or make the adopted normalization a theorem. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-135 · Draft id G-188", "url": "/library-v2/LIB2-184/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-185", "title": "The rank-two support certificate excludes a rank-five extension at the MOS tier", "text": "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. · Caution: The support certificate does not exclude a microscopic map outside the printed quotient tier or deny the ambient rank-five construction. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-135 · Draft id G-189", "url": "/library-v2/LIB2-185/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-186", "title": "The unit grade-four response is a declared premise", "text": "PREMISE-GRADE-4-RESPONSE fixes |λµ| = 1 on the transported record quotient and removes its positive amplitude modulus while leaving τ = ±1 unselected. · Caution: The premise does not construct Πfull, prove a microscopic grade-four readout, select the torsor side or derive a CKM quantity. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-131 · Draft id G-190", "url": "/library-v2/LIB2-186/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-187", "title": "The unadopted response alternatives retain distinct meanings", "text": "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. · Caution: Neither alternative enters the physical spectral-pair gate, and declining an isometry premise does not fix the response to zero. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-131 · Draft id G-191", "url": "/library-v2/LIB2-187/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-188", "title": "The registered free quaternionic fermion determinant is non-negative", "text": "On the registered orthonormalized branch module, det(mI + D) = m⁸(m² + 3)⁸ gives the source's free quaternionic fermion positivity. · Caution: This free-sector result does not construct the required interacting chiral determinant-line trivialization. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-094 · Draft id G-192", "url": "/library-v2/LIB2-188/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-189", "title": "The anisotropic heat-kernel family has nonlinear OS positivity in its cone", "text": "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. · Caution: This family-specific reflection positivity does not establish a general gravitational measure or a continuum Einstein limit. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-094 · Draft id G-193", "url": "/library-v2/LIB2-189/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-190", "title": "No positive path in the declared heat-kernel family reaches pure MM/EH", "text": "No continuous positive path in the declared anisotropic heat-kernel family reaches the pure MacDowell–Mansouri/Einstein–Hilbert weight. · Caution: This excludes only the stated path in this family, not a nonlinear simplicity-constrained completion. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-095 · Draft id G-194", "url": "/library-v2/LIB2-190/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-191", "title": "The stated bivector simplicity condition cannot be imposed by a linear projector", "text": "The source's sum of two simple bivectors has rank 4, so a linear projector cannot impose the stated bivector simplicity condition. · Caution: This obstruction does not exclude nonlinear simplicity measures or prove that such a measure has an Einstein limit. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-094 · Draft id G-195", "url": "/library-v2/LIB2-191/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-192", "title": "A positive nonlinear simplicity measure exists at finite regulator", "text": "The stated fixed-norm Pfaffian variety with a coercive quartic admits a positive nonlinear simplicity measure at finite regulator, with reflection positivity supplied by paired multiplication operators. · Caution: Finite-regulator existence does not establish Einstein universality or the continuum renormalization-group limit. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-094 · Draft id G-196", "url": "/library-v2/LIB2-192/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-193", "title": "The registered Clifford construction has a one-particle bare gap", "text": "The registered one-particle gap is MN = Λ√(ϕ^(2N) + 1/4), with χlocal² = 1/4 only inside the attachment; the interacting pole, LSZ and occupancy remain open. · Caution: The bare gap does not derive an interacting rest mass, physical occupation or a successful exact single-χ ratio law. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-090 · Draft id G-197", "url": "/library-v2/LIB2-193/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-194", "title": "The frozen Clifford law makes every registered carrier-map Gram isotropic", "text": "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. · Caution: The identity does not identify a physical measurement or transfer a constant to a different carrier through an unconstructed map. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-103 · Draft id G-198", "url": "/library-v2/LIB2-194/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-195", "title": "The frozen symplectic braid representation has a nonscalar centre", "text": "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). · Caution: The representation does not supply the missing functor to the winding category or identify the trace-three word with a physical lepton neck. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-104 · Draft id G-199", "url": "/library-v2/LIB2-195/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-196", "title": "The specified classical vacuum spectrum is reproduced by CSS charge sums", "text": "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. · Caution: The conditional classical-spectrum closure is not quantum stability, a Standard-Model mass spectrum or an independently verified world-facing prediction. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-042 · Draft id G-200", "url": "/library-v2/LIB2-196/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-197", "title": "The positive congruence dressing stays inside the registered E7 group", "text": "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). · Caution: The closure theorem does not apply to arbitrary Gram matrices or derive a physical mass or observation-map attachment. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-035 · Draft id G-201", "url": "/library-v2/LIB2-197/", "source": "v2 · CLAIM · H01 · DRAFTED"}, {"id": "LIB2-198", "title": "The MRSS Higgs parity is unique only under the loaded scalar spectrum", "text": "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. · Caution: Uniqueness given the desired scalar content does not derive that content or remove its circularity risk. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-041 · Draft id G-202", "url": "/library-v2/LIB2-198/", "source": "v2 · CLAIM · H05 · DRAFTED"}, {"id": "LIB2-199", "title": "The weak-angle value remains a structural target on a scheme-dependent curve", "text": "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. · Caution: The target does not select a matching scale or supply a scheme-matched electroweak precision prediction. · Labels as printed: Structural / NOT_PRINTED · Candidates: C2-014 · Draft id G-203", "url": "/library-v2/LIB2-199/", "source": "v2 · CLAIM · H04 · DRAFTED"}, {"id": "LIB2-200", "title": "The AX6 polarization postulate gives its readout without selecting itself", "text": "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. · Caution: The readout identity does not derive AX6pol or the low-energy matching scale, and the retired Det2 argument does not select it. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-125 · Draft id G-204", "url": "/library-v2/LIB2-200/", "source": "v2 · CLAIM · H02 · DRAFTED"}, {"id": "LIB2-201", "title": "The parked moment model records a traversal with sixty winding ticks", "text": "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. · Caution: The parked winding count does not predict an observed duration in seconds or promote the moment interpretation to a physical result. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-167 · Draft id G-205", "url": "/library-v2/LIB2-201/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-202", "title": "The specified constant set cannot supply a duration in seconds", "text": "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. · Caution: The restricted dimensional obstruction does not exclude adding an external time axis or establish a measured clock period. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-167 · Draft id G-206", "url": "/library-v2/LIB2-202/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-203", "title": "The parked Gogberashvili splice imports an external time axis", "text": "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. · Caution: The splice does not derive its external time-axis inputs or resolve time calibration from the banked constant set alone. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-167 · Draft id G-207", "url": "/library-v2/LIB2-203/", "source": "v2 · CLAIM · H07 · DRAFTED"}, {"id": "LIB2-204", "title": "SL-01: NuFIT solar mass-squared splitting comparator", "text": "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. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-179 · Draft id G-208", "url": "/library-v2/LIB2-204/", "source": "v2 · COMPARATOR · H08 · DRAFTED"}, {"id": "LIB2-205", "title": "SL-02: NuFIT atmospheric splitting with SK-ATM", "text": "The ledger’s normal-ordering NuFIT atmospheric mass-squared splitting comparator with SK-ATM is 2.511e-3 eV², with asymmetric uncertainties. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-180 · Draft id G-209", "url": "/library-v2/LIB2-205/", "source": "v2 · COMPARATOR · H08 · DRAFTED"}, {"id": "LIB2-206", "title": "SL-03: NuFIT atmospheric splitting without SK-ATM", "text": "The ledger records the normal-ordering NuFIT atmospheric mass-squared splitting without SK-ATM, with asymmetric uncertainties. · Candidates: C2-181 · Draft id G-210", "url": "/library-v2/LIB2-206/", "source": "v2 · COMPARATOR · H08 · DRAFTED"}, {"id": "LIB2-207", "title": "SL-04: DESI baseline neutrino-mass-sum upper bound", "text": "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. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-182 · Draft id G-211", "url": "/library-v2/LIB2-207/", "source": "v2 · COMPARATOR · H08 · DRAFTED"}, {"id": "LIB2-208", "title": "SL-05: DESI Feldman–Cousins neutrino-mass-sum upper bound", "text": "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. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-183 · Draft id G-212", "url": "/library-v2/LIB2-208/", "source": "v2 · COMPARATOR · H08 · DRAFTED"}, {"id": "LIB2-209", "title": "SL-06: MS-bar weak-angle comparator at the Z scale", "text": "The ledger’s MS-bar weak-angle comparator at MZ is sin²θ̂W = 0.23122 ± 0.00006. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-184 · Draft id G-213", "url": "/library-v2/LIB2-209/", "source": "v2 · COMPARATOR · H08 · DRAFTED"}, {"id": "LIB2-210", "title": "SL-07: MS-bar strange Yukawa comparator", "text": "The ledger records the strange-quark Yukawa coupling in the MS-bar scheme at its stated teraelectronvolt scale, with asymmetric uncertainties. · Candidates: C2-185 · Draft id G-214", "url": "/library-v2/LIB2-210/", "source": "v2 · COMPARATOR · H08 · DRAFTED"}, {"id": "LIB2-211", "title": "SL-08: MS-bar bottom Yukawa comparator", "text": "The ledger records the bottom-quark Yukawa coupling in the MS-bar scheme at its stated teraelectronvolt scale, with asymmetric uncertainties. · Candidates: C2-186 · Draft id G-215", "url": "/library-v2/LIB2-211/", "source": "v2 · COMPARATOR · H08 · DRAFTED"}, {"id": "LIB2-212", "title": "SL-09: Global-fit CKM Dirac phase in radians", "text": "The ledger’s global-fit CKM Dirac-phase comparator is δ = 1.154 ± 0.025 rad. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-187 · Draft id G-216", "url": "/library-v2/LIB2-212/", "source": "v2 · COMPARATOR · H08 · DRAFTED"}, {"id": "LIB2-213", "title": "SL-10: Global-fit Jarlskog invariant comparator", "text": "The ledger’s global-fit Jarlskog comparator is J = 3.16e-5, with asymmetric errors +0.13e-5 and −0.11e-5. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-188 · Draft id G-217", "url": "/library-v2/LIB2-213/", "source": "v2 · COMPARATOR · H08 · DRAFTED"}, {"id": "LIB2-214", "title": "SL-11: First-row Cabibbo-magnitude comparator", "text": "The ledger’s first-row-average comparator for |Vus| is 0.22431 ± 0.00085. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-189 · Draft id G-218", "url": "/library-v2/LIB2-214/", "source": "v2 · COMPARATOR · H08 · DRAFTED"}, {"id": "LIB2-215", "title": "SL-12: Retained PDG |Vub| comparator", "text": "The ledger’s retained comparator for |Vub| is 0.00389 ± 0.00016. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-190 · Draft id G-219", "url": "/library-v2/LIB2-215/", "source": "v2 · COMPARATOR · H08 · DRAFTED"}, {"id": "LIB2-216", "title": "SL-13: Retained PDG |Vcb| comparator", "text": "The ledger’s retained comparator for |Vcb| is 0.0407 ± 0.0013. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-191 · Draft id G-220", "url": "/library-v2/LIB2-216/", "source": "v2 · COMPARATOR · H08 · DRAFTED"}, {"id": "LIB2-217", "title": "SL-14: First-row |Vud| comparator", "text": "The ledger’s first-row comparator for |Vud| is 0.97367 ± 0.00032. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-192 · Draft id G-221", "url": "/library-v2/LIB2-217/", "source": "v2 · COMPARATOR · H08 · DRAFTED"}, {"id": "LIB2-218", "title": "SL-15: MS-bar charm mass at its self-scale", "text": "The ledger’s MS-bar charm-mass comparator at the charm self-scale is mc(mc) = 1272.9 ± 4.5 MeV. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-193 · Draft id G-222", "url": "/library-v2/LIB2-218/", "source": "v2 · COMPARATOR · H08 · DRAFTED"}, {"id": "LIB2-219", "title": "SL-16: MS-bar bottom mass at its self-scale", "text": "The ledger’s MS-bar bottom-mass comparator at the bottom self-scale is mb(mb) = 4186 ± 6 MeV. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-194 · Draft id G-223", "url": "/library-v2/LIB2-219/", "source": "v2 · COMPARATOR · H08 · DRAFTED"}, {"id": "LIB2-220", "title": "SL-17: Direct/MC top-mass comparator", "text": "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. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-195 · Draft id G-224", "url": "/library-v2/LIB2-220/", "source": "v2 · COMPARATOR · H08 · DRAFTED"}, {"id": "LIB2-221", "title": "SL-18: Measured tau-mass anchor", "text": "The ledger’s measured tau-mass anchor is mτ = 1776.93 ± 0.09 MeV. · Labels as printed: Input / NOT_PRINTED · Candidates: C2-196 · Draft id G-225", "url": "/library-v2/LIB2-221/", "source": "v2 · COMPARATOR · H08 · DRAFTED"}, {"id": "LIB2-222", "title": "SL-19: Global-fit CKM Dirac phase in degrees", "text": "The ledger’s degree presentation of the global-fit CKM Dirac phase is δ = 66.12° ± 1.43°. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-197 · Draft id G-226", "url": "/library-v2/LIB2-222/", "source": "v2 · COMPARATOR · H08 · DRAFTED"}, {"id": "LIB2-223", "title": "SL-20: Direct unitarity-triangle angle comparator", "text": "The ledger’s direct unitarity-triangle angle comparator is γ = 66.4° with asymmetric errors +2.7° and −2.8°. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-198 · Draft id G-227", "url": "/library-v2/LIB2-223/", "source": "v2 · COMPARATOR · H08 · DRAFTED"}, {"id": "LIB2-224", "title": "SL-21: On-shell weak-angle comparator", "text": "The ledger’s on-shell weak-angle comparator is 0.22348 ± 0.00010. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-199 · Draft id G-228", "url": "/library-v2/LIB2-224/", "source": "v2 · COMPARATOR · H08 · DRAFTED"}, {"id": "LIB2-225", "title": "SL-22: Effective-leptonic weak-angle comparator", "text": "The ledger’s effective-leptonic weak-angle comparator is 0.23161 ± 0.00004. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-200 · Draft id G-229", "url": "/library-v2/LIB2-225/", "source": "v2 · COMPARATOR · H08 · DRAFTED"}, {"id": "LIB2-226", "title": "SL-23: NuFIT squared-sine reactor-angle comparator", "text": "The ledger’s normal-ordering squared-sine reactor-angle comparator is 0.02248 with asymmetric errors +0.00055 and −0.00059. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-201 · Draft id G-230", "url": "/library-v2/LIB2-226/", "source": "v2 · COMPARATOR · H08 · DRAFTED"}, {"id": "LIB2-227", "title": "SL-24: NuFIT solar angle in degrees", "text": "The ledger’s normal-ordering solar-angle comparator is 33.76° with asymmetric errors +0.42° and −0.41°. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-202 · Draft id G-231", "url": "/library-v2/LIB2-227/", "source": "v2 · COMPARATOR · H08 · DRAFTED"}, {"id": "LIB2-228", "title": "SL-26: NuFIT reactor angle in degrees", "text": "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. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-204 · Draft id G-232", "url": "/library-v2/LIB2-228/", "source": "v2 · COMPARATOR · H08 · DRAFTED"}, {"id": "LIB2-229", "title": "SL-27: House-computed candidate coefficient diagnostic", "text": "The ledger’s house-computed, scheme-dependent coefficient diagnostic is 4.9635 ± 0.087; it is not a PDG measurement. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-205 · Draft id G-233", "url": "/library-v2/LIB2-229/", "source": "v2 · COMPARATOR · H08 · DRAFTED"}, {"id": "LIB2-230", "title": "SL-28: Historical PDG |Vcb| comparator", "text": "The historical comparator for |Vcb| was 0.0408 ± 0.0014 and is retained only as the earlier value in the printed comparator transition. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-206 · Draft id G-234", "url": "/library-v2/LIB2-230/", "source": "v2 · COMPARATOR · H08 · DRAFTED"}, {"id": "LIB2-231", "title": "SL-29: Historical PDG |Vub| comparator", "text": "The historical comparator for |Vub| was 0.00382 ± 0.00024 and is retained only as the earlier value in the printed comparator transition. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-207 · Draft id G-235", "url": "/library-v2/LIB2-231/", "source": "v2 · COMPARATOR · H08 · DRAFTED"}, {"id": "LIB2-232", "title": "SL-30: Global-fit Jarlskog comparator in the printed scaled units", "text": "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. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-208 · Draft id G-236", "url": "/library-v2/LIB2-232/", "source": "v2 · COMPARATOR · H08 · DRAFTED"}, {"id": "LIB2-233", "title": "Retired blanket zero-parameter observable headline", "text": "The archived observable summary presented a blanket zero-parameter headline. · Caution: Retiring the blanket headline does not refute each formula or erase the explicitly loaded map's internal parameter economy. · Candidates: C2-098 · Draft id G-237", "url": "/library-v2/LIB2-233/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-234", "title": "Retired 20/20 Standard-Model completion headline", "text": "The archived strange-sector proof title advertised completion of the Standard-Model observable ledger. · Caution: This retirement concerns the completion headline, not a claim that every archived calculation or the current strange proxy is false. · Candidates: C2-023 · Draft id G-238", "url": "/library-v2/LIB2-234/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-235", "title": "Superseded three-of-eight mixing tally and pending atmospheric hold", "text": "The earlier mixing summary retained a three-of-eight tally while the physical atmospheric-octant attachment remained on a pending hold. · Caution: The retyped physical tally leaves the internal mismatch identity and its numerical value unchanged. · Candidates: C2-098 · Draft id G-239", "url": "/library-v2/LIB2-235/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-236", "title": "Retired Wyler bounded-domain derivation of alpha", "text": "The earlier bounded-domain programme presented Wyler normalization as a derivation of the electromagnetic fine-structure constant. · Caution: The physical-route retirement does not declare every Wyler evaluation, class identity or boundary-volume calculation mathematically false. · Candidates: C2-137 C2-153 C2-175 · Draft id G-240", "url": "/library-v2/LIB2-236/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-237", "title": "Retired exact-framework Cabibbo correction 0.225247", "text": "The earlier hand-calculated correction presented |Vus| = 0.225247 as the exact-framework Cabibbo readout. · Caution: Correcting the decimal does not derive the loaded route choice or change the separate exact block weight. · Candidates: C2-009 C2-062 · Draft id G-241", "url": "/library-v2/LIB2-237/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-238", "title": "Superseded rounded-angle Cabibbo value as the canonical readout", "text": "The earlier canonical Cabibbo display used 0.225268, obtained from the rounded solar angle 33.49°. · Caution: The rounded-input evaluation remains a distinct diagnostic; only its use as the canonical exact-framework value is superseded. · Candidates: C2-009 · Draft id G-242", "url": "/library-v2/LIB2-238/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-239", "title": "Deprecated house Cabibbo-comparator route", "text": "The earlier house Cabibbo entry presented its algebraic-comparator route as operative; its supplied header now flags that route as deprecated. · Caution: This retirement does not retire the current loaded Route-B formula merely because both descriptions use the Route-B name. · Candidates: C2-147 · Draft id G-243", "url": "/library-v2/LIB2-239/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-240", "title": "Retired Shilov atmospheric-angle derivation", "text": "The earlier atmospheric-angle route presented a Shilov-boundary correction as the operative prediction. · Caution: The old arctangent target is not the separate retired rational target, and the new physical branch remains a loaded correspondence. · Candidates: C2-168 · Draft id G-244", "url": "/library-v2/LIB2-240/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-241", "title": "Retired claim that the chirality interface selected the atmospheric octant", "text": "The earlier atmospheric account claimed that the chirality interface had built the octant selector and locked the branch, thereby reducing the free-bit count. · Caution: The retirement leaves the internal mismatch identity intact and does not select the opposite physical octant. · Candidates: C2-005 C2-059 · Draft id G-245", "url": "/library-v2/LIB2-241/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-242", "title": "Superseded trimaximal cosine-phase correction apparatus", "text": "The house once carried a cosine-phase correction within the now-superseded trimaximal mixing apparatus. · Caution: Supersession of the apparatus does not show that the historical erratum was mathematically incorrect. · Candidates: C2-152 · Draft id G-246", "url": "/library-v2/LIB2-242/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-243", "title": "Superseded trimaximal condition and rho-modulus apparatus", "text": "The house once carried a trimaximal condition and rho modulus requiring an extra postulate as part of its mixing apparatus. · Caution: Retiring this apparatus does not refute its stated postulate independence or derive all current mixing attachments. · Candidates: C2-173 · Draft id G-247", "url": "/library-v2/LIB2-243/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-244", "title": "Superseded hybrid leptonic-phase formula", "text": "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. · Caution: The replacement readout remains conditional and does not establish equivalence between the old hybrid expression and other phase formulas. · Candidates: C2-159 · Draft id G-248", "url": "/library-v2/LIB2-244/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-245", "title": "Retired physical use of the PSL class-algebra sign argument", "text": "The earlier class-algebra argument used a vanishing structure constant to select the sign of a leptonic phase formula. · Caution: The pure class-algebra constants survive, and the old phase expression remains only as a labelled cross-check. · Candidates: C2-172 · Draft id G-249", "url": "/library-v2/LIB2-245/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-246", "title": "Retired legacy baryon-to-meson mass ratio", "text": "The earlier ambient-Hessian calculation presented a baryon/meson mass ratio of approximately 6.7 as reproducing one hadron ratio. · Caution: The numerical retirement does not retire the separate tensor-structure statement that the cubic baryonic channel survives the quadratic cancellation. · Candidates: C2-142 · Draft id G-250", "url": "/library-v2/LIB2-246/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-247", "title": "Withdrawn proof and zero-parameter status of the muon-to-tau ratio", "text": "The earlier charged-lepton account classified the muon-to-tau ratio as proved and carrying zero free parameters. · Caution: The typing is withdrawn while the ratio remains a structural loaded correspondence with its numerical reproduction intact. · Candidates: C2-018 C2-056 · Draft id G-251", "url": "/library-v2/LIB2-247/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-248", "title": "Withdrawn universal two-parameter mass-completion no-go", "text": "The earlier mass-completion account claimed that every completion with at most two parameters was impossible. · Caution: Withdrawing the universal claim does not rescue the exact single-chi class or make the fitted harmonic a derived replacement law. · Candidates: C2-055 · Draft id G-252", "url": "/library-v2/LIB2-248/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-249", "title": "Retired Det-squared selection of the polarization postulate", "text": "The former weak-angle account used the Det-squared construction as the selector of the independent polarization postulate. · Caution: The retirement does not refute the separate Galois argument or derive the polarization postulate and its physical matching scale. · Candidates: C2-125 · Draft id G-253", "url": "/library-v2/LIB2-249/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-250", "title": "Withdrawn Schur-only proof of vanishing triplet masses", "text": "The earlier proof sketch inferred vanishing triplet entries at every loop order from Schur block structure alone. · Caution: The withdrawn proof does not remove Schur block structure or independently overturn the reported numerical zeros. · Candidates: C2-114 · Draft id G-254", "url": "/library-v2/LIB2-250/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-251", "title": "Scoped withdrawal of blanket Artin protection for Yukawa loops", "text": "The earlier renormalization claim treated Yukawa and gauge running as fully protected by Artin without a diagram-by-diagram internal-generator census. · Caution: This scope withdrawal does not deny associativity for two-generated subalgebras or refute the separately specified lepton–photon sector. · Candidates: C2-114 · Draft id G-255", "url": "/library-v2/LIB2-251/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-252", "title": "Withdrawn canonical reactor half-angle from the moment law", "text": "Earlier wording treated the reactor half-angle as canonical solely by appeal to the symplectic moment half-turn law. · Caution: The retraction leaves the moment law and the numerical reactor formula intact while withholding a derivation of its readout rule. · Candidates: C2-006 C2-060 · Draft id G-256", "url": "/library-v2/LIB2-252/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-253", "title": "Retired structural derivation rating of the CKM phase construction", "text": "The earlier CKM phase account gave its readout-conditioned construction a structural derivation rating despite the missing selection of its correction term. · 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. · Candidates: C2-012 C2-065 · Draft id G-257", "url": "/library-v2/LIB2-253/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-254", "title": "Withdrawn universal claim that inequality conditions cannot reduce dimension", "text": "The earlier selector argument ruled out every positivity or stability refinement on the premise that 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. · Candidates: C2-121 · Draft id G-258", "url": "/library-v2/LIB2-254/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-255", "title": "Retired use of one operator name for Wick chart and shell reversal", "text": "The earlier geometry account treated the single label W as covering both the compact/split Wick chart and the shell-orientation reversal. · Caution: Retiring the shared name does not invalidate either separated operator or identify their actions on the grading. · Candidates: C2-089 · Draft id G-259", "url": "/library-v2/LIB2-255/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-256", "title": "Superseded nontrivial bundle reading of the signature sheets", "text": "The earlier signature-sheet account described the two real-form presentations as a nontrivial bundle rather than a real-form correspondence. · Caution: This replacement does not deny the separately priced reduced clutching class or construct a physical observation map. · Candidates: C2-089 · Draft id G-260", "url": "/library-v2/LIB2-256/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-257", "title": "Retired one-bit accounting of distinct gluing and observation structures", "text": "The earlier accounting charged local overlap, global holonomy, real-form correspondence and physical observation as one W bit. · Caution: Separating the accounting does not construct the observation map or determine a total physical freedom count. · Candidates: C2-088 · Draft id G-261", "url": "/library-v2/LIB2-257/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-258", "title": "Retired finite-sign chamber-lift price computed on the wrong carrier", "text": "The earlier chamber-lift row inferred a finite orthogonal-sign ambiguity from a commutant calculated on the wrong permutation carrier. · Caution: The corrected complement-frame gauge does not add continuous observable freedom or select the microscopic observation functor. · Candidates: C2-093 · Draft id G-262", "url": "/library-v2/LIB2-258/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-259", "title": "Withdrawn aggregate bit-and-dimension freedom headline", "text": "The earlier freedom ledger combined a bit total, a dimension count and a surplus into one headline before computing the observation-functor faithfulness kernel. · Caution: The withdrawal does not erase the separately typed data or license a replacement scalar total without a faithfulness analysis. · Candidates: C2-088 C2-067 · Draft id G-263", "url": "/library-v2/LIB2-259/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-260", "title": "Retired microscopic selector-deriving status of the earlier parent action", "text": "The earlier microscopic-parent account claimed that its root-line minimum fixed every coefficient without an unselected marking or orientation branch. · Caution: The demotion does not make the loaded finite action algebraically inconsistent or close the physical parent-action problem. · Candidates: C2-105 · Draft id G-264", "url": "/library-v2/LIB2-260/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-261", "title": "Retired independent-channel source doorway", "text": "The earlier source model treated the two channel patterns as independent rather than as the images of one common selector contrast. · Caution: The paired-source replacement does not select the common contrast or remove the separate arrow-selection problem. · Candidates: C2-105 · Draft id G-265", "url": "/library-v2/LIB2-261/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-262", "title": "Withdrawn unconditional action preference for the root line", "text": "The earlier selector account said the action voted for the root line without carrying the common-lift condition required by that preference. · Caution: The correction neither selects the relative lift axis nor contradicts the explicitly conditional root-line result. · Candidates: C2-105 · Draft id G-266", "url": "/library-v2/LIB2-262/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-263", "title": "Retired depth-exclusion inference from commuting charge and mass", "text": "The earlier depth-exclusion cut treated commutation of the mass and electromagnetic charge operators as forbidding depth sourcing. · Caution: Withdrawing the cut does not identify the two clock labels or select depth or order as the physical source. · Candidates: C2-068 · Draft id G-267", "url": "/library-v2/LIB2-263/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-264", "title": "Withdrawn claim that the promotion functional was constructed and run", "text": "The earlier promotion-gate account said its canonical test functional was constructed and its zero set house-verified at the required operator tier. · 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. · Candidates: C2-067 C2-088 · Draft id G-268", "url": "/library-v2/LIB2-264/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-265", "title": "Superseded Wyler-baseline route for the muon mass", "text": "The archived muon prompts proposed identifying the muon mass with a Wyler baseline. · Caution: Replacing the physical baseline does not refute a numerical Wyler evaluation or make the current loaded ratio a derivation. · Candidates: C2-018 C2-056 · Draft id G-269", "url": "/library-v2/LIB2-265/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-266", "title": "Superseded electromagnetic-power Wyler formula for the muon", "text": "The archive presented an electromagnetic-power Wyler expression as a closed muon-mass formula. · Caution: The replacement does not establish that every algebraic operation in the old formula was false or that the present normalization is forced. · Candidates: C2-018 C2-056 · Draft id G-270", "url": "/library-v2/LIB2-266/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-267", "title": "Superseded sub-Wyler route for the electron mass", "text": "The archived electron prompts proposed a sub-Wyler mass route, with the proof prompt attributing it to the minimal orbit. · Caution: The current electron chain still needs the external empirical Koide rule, the measured tau anchor and the loaded muon chain. · Candidates: C2-020 C2-057 · Draft id G-271", "url": "/library-v2/LIB2-267/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-268", "title": "Superseded extended-Wyler route for the tau mass", "text": "The archived tau prompts proposed an extended-Wyler mass formula, with the proof title also naming a sum of dimensions. · Caution: The use of a measured tau anchor does not falsify the archived dimension identity or supply an algebra-only tau-mass prediction. · Candidates: C2-113 · Draft id G-272", "url": "/library-v2/LIB2-268/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-269", "title": "Superseded Peirce-cylinder proposal for the tau mass", "text": "The archive proposed obtaining the tau mass from the muon mass through a power of a Peirce-cylinder ratio. · Caution: Replacing the proposed physical formula does not exclude every cylinder relation or turn the measured tau anchor into a prediction. · Candidates: C2-113 · Draft id G-273", "url": "/library-v2/LIB2-269/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-270", "title": "Superseded D-tower formula for the bottom mass", "text": "The archived bottom-mass prompt proposed a D-tower golden-power formula as its physical mass target. · Caution: The current bridge remains a boundary-value correspondence with a status-ineligible cross-scheme comparison, not a low-energy mass theorem. · Candidates: C2-021 · Draft id G-274", "url": "/library-v2/LIB2-270/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-271", "title": "Superseded pi-weighted prefactor formula for the bottom mass", "text": "The archived numerical bottom-mass prompt proposed a cylinder-prefactor expression multiplied by a fractional power of pi. · Caution: The replacement is not a re-evaluation of the archived prefactor and does not supply the missing scheme-matched physical bridge. · Candidates: C2-021 · Draft id G-275", "url": "/library-v2/LIB2-271/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-272", "title": "Superseded cylinder-prefactor proof prompt for the bottom mass", "text": "The archived proof prompt proposed deriving the bottom-mass prefactor from the Peirce cylinder. · Caution: A title-level replacement does not establish that the absent prefactor proof was executed or mathematically disproved. · Candidates: C2-021 · Draft id G-276", "url": "/library-v2/LIB2-272/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-273", "title": "Superseded D-tower formula for the charm mass", "text": "The archived charm-mass prompt proposed a D-tower golden-power formula as its physical mass target. · Caution: The current constituent-anchored comparison is not a scheme-matched mass theorem or a refutation of every tower construction. · Candidates: C2-022 · Draft id G-277", "url": "/library-v2/LIB2-273/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-274", "title": "Superseded triality log-geometric-mean charm formula", "text": "The archived triality proposal obtained the charm mass from a geometric combination of the muon and top masses. · Caution: The current target replaces this physical formula without proving that every triality identity in its absent derivation was false. · Candidates: C2-022 · Draft id G-278", "url": "/library-v2/LIB2-274/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-275", "title": "Superseded cubic-to-tower triality bridge for the charm mass", "text": "The archived charm proof prompt proposed a triality bridge from the Jordan cubic to a D-tower. · Caution: The title-level replacement neither reconstructs the old cubic bridge nor makes the current physical mass export a theorem. · Candidates: C2-022 · Draft id G-279", "url": "/library-v2/LIB2-275/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-276", "title": "Superseded resummed-electromagnetic charm formula", "text": "The archived charm prompt proposed obtaining its mass from the top mass and a resummed electromagnetic-coupling factor. · Caution: Replacing this formula does not establish a general electromagnetic-resummation no-go or complete the present mass-scheme conversion. · Candidates: C2-022 · Draft id G-280", "url": "/library-v2/LIB2-276/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-277", "title": "Superseded early cubic-phase ansatz for the leptonic Dirac phase", "text": "The early PMNS phase prompts proposed a cubic-invariant ansatz as the leptonic Dirac-phase target. · Caution: The new target remains conditional on its readout premises; replacement does not prove that the archived prompt contained a completed derivation. · Candidates: C2-007 C2-061 · Draft id G-281", "url": "/library-v2/LIB2-277/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-278", "title": "Superseded imaginary-correction prompt for the leptonic phase", "text": "The archived numerical prompt proposed an imaginary-correction term to adjust the leptonic Dirac phase toward a benchmark. · Caution: Replacing this correction prompt does not derive the physical readout map or establish a universal exclusion of phase corrections. · Candidates: C2-007 C2-061 · Draft id G-282", "url": "/library-v2/LIB2-278/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-279", "title": "Superseded determinant-imaginary-part route for the full leptonic phase", "text": "The archived extension prompt proposed obtaining the full leptonic Dirac phase from the imaginary part of the Jordan determinant. · Caution: This replacement neither reconstructs the absent determinant-phase proof nor removes the conditions on the current phase attachment. · Candidates: C2-007 C2-061 · Draft id G-283", "url": "/library-v2/LIB2-279/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-280", "title": "Superseded sum-rule and torsion-corrected reactor route to the leptonic phase", "text": "The archived phase prompt proposed a sum-rule readout using a torsion-corrected reactor angle. · Caution: The replacement does not refute an unspecified sum-rule identity or turn the current reactor and phase readouts into unconditional predictions. · Candidates: C2-007 C2-061 · Draft id G-284", "url": "/library-v2/LIB2-280/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-281", "title": "Superseded cylinder formula for the reactor angle", "text": "The archived reactor-angle prompt proposed an electromagnetic-power arctangent from the Peirce cylinder as its mixing-angle target. · Caution: The current reactor expression retains an unforced readout premise; replacing the older target does not prove a universal cylinder-model exclusion. · Candidates: C2-006 C2-060 · Draft id G-285", "url": "/library-v2/LIB2-281/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-282", "title": "Superseded torsion-corrected cylinder formula for the reactor angle", "text": "The archived reactor-angle proof prompt advertised an exact target obtained by subtracting a torsion correction from the cylinder arctangent. · Caution: This replacement does not establish the old correction's value or make the current readout rule canonical. · Candidates: C2-006 C2-060 · Draft id G-286", "url": "/library-v2/LIB2-282/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-283", "title": "Superseded torsion-corrected PMNS angle scheme", "text": "The archived PMNS-angle prompt proposed a torsion-corrected scheme combining quark–lepton complementarity, Shilov and split-G2 contributions. · Caution: The current mixed-provenance angle set does not refute every torsion correction or derive the physical readout and octant choices. · Candidates: C2-004 C2-005 C2-006 C2-058 C2-059 C2-060 · Draft id G-287", "url": "/library-v2/LIB2-283/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-284", "title": "Superseded Shilov-circle correction prompt for the atmospheric angle", "text": "The archived atmospheric-angle proof prompt proposed a Shilov-circle correction as its physical angle construction. · Caution: The present lower-octant target is a loaded correspondence, and this replacement does not refute every Shilov-circle identity. · Candidates: C2-005 C2-059 · Draft id G-288", "url": "/library-v2/LIB2-284/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-285", "title": "Superseded Peirce golden-power assignment for two CKM magnitudes", "text": "The archived Peirce-sector proposal assigned the two smaller CKM magnitudes through successive powers of a common mixing parameter divided by the golden ratio. · Caution: The current magnitude formulas remain loaded and do not derive the physical CKM matrix from the bare algebra. · Candidates: C2-010 C2-011 C2-063 C2-064 · Draft id G-289", "url": "/library-v2/LIB2-285/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-286", "title": "Superseded additive correction prompt for Vcb", "text": "The archived numerical prompt proposed an additive correction to the Vcb target using its beta-delta coefficient. · Caution: The replacement does not derive the current integer choice or establish that every proposed correction is excluded. · Candidates: C2-010 C2-063 · Draft id G-290", "url": "/library-v2/LIB2-286/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-287", "title": "Superseded golden-power ratio of CKM hierarchy magnitudes", "text": "The archived hierarchy proposals identified the Vub-to-Vcb magnitude ratio with a fixed negative power of the golden ratio. · Caution: This replaces the physical hierarchy ratio only and leaves the separate Rb subclaim unadjudicated. · Candidates: C2-011 C2-064 · Draft id G-291", "url": "/library-v2/LIB2-287/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-288", "title": "Superseded Cabibbo-squared formula for Vcb", "text": "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. · Caution: Replacing this historical formula does not select the present physical attachment or the unforced integer in its denominator. · Candidates: C2-010 C2-063 · Draft id G-292", "url": "/library-v2/LIB2-288/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-289", "title": "Superseded reciprocal weak-angle proposal", "text": "The archived weak-angle prompt proposed a reciprocal expression involving the golden ratio as its physical target. · Caution: The current weak-angle target still requires its independent polarization premise and a derived matching scale. · Candidates: C2-014 · Draft id G-293", "url": "/library-v2/LIB2-289/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-290", "title": "Superseded logarithmic loop-correction prompt for the weak angle", "text": "The archived numerical prompt proposed a logarithmic one-loop correction to adjust the weak-angle value toward its comparator. · Caution: The current scope does not exclude every electroweak loop correction or provide the missing scale and threshold calculation. · Candidates: C2-014 · Draft id G-294", "url": "/library-v2/LIB2-290/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-291", "title": "Superseded cylinder-running proof prompt for the weak angle", "text": "The archived proof prompt proposed obtaining the weak angle from one-loop Peirce-cylinder running. · Caution: The replacement does not refute all cylinder-running models or derive a completed Z-pole prediction. · Candidates: C2-014 · Draft id G-295", "url": "/library-v2/LIB2-291/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-292", "title": "Superseded electromagnetic-subtraction formula for the weak angle", "text": "The archived weak-angle proof prompt proposed an electromagnetic subtraction from the golden tree target as a one-loop correction. · Caution: The current structural target is not a completed radiative prediction, and the replacement does not exclude all electromagnetic corrections. · Candidates: C2-014 · Draft id G-296", "url": "/library-v2/LIB2-292/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-293", "title": "Superseded QLC-plus-cylinder correction for the Cabibbo angle", "text": "The archived numerical prompt proposed adding a cylinder-based arctangent correction to a quark–lepton-complementarity Cabibbo value. · Caution: The current framework-angle readout remains route-selected by data and does not derive the physical first-row map. · Candidates: C2-009 C2-062 · Draft id G-297", "url": "/library-v2/LIB2-293/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-294", "title": "Superseded torsion-corrected Cabibbo–Weinberg formula", "text": "The archived Cabibbo proof prompt proposed an arctangent of the golden weak-angle expression followed by a torsion subtraction. · Caution: Replacing this formula neither selects the current first-row route nor solves the weak-angle matching problem. · Candidates: C2-009 C2-062 · Draft id G-298", "url": "/library-v2/LIB2-294/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-295", "title": "Superseded Cabibbo–Weinberg residual identity as a physical target", "text": "The archived proof prompt proposed equating a Cabibbo–Weinberg residual with an electromagnetic expression. · Caution: The current separate readouts do not supply a scheme-matched test or a universal refutation of the old residual relation. · Candidates: C2-009 C2-014 C2-062 · Draft id G-299", "url": "/library-v2/LIB2-295/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-296", "title": "Superseded singular-vacuum premise of the protection-and-bounce chain", "text": "The archived protection-and-bounce chain assumed a vanishing determinant and a vanishing third eigenvalue at the working vacuum. · Caution: The normalization replacement does not exclude singular Jordan elements or independently adjudicate the old Z-mass protection and bounce implications. · Candidates: C2-002 · Draft id G-300", "url": "/library-v2/LIB2-296/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-297", "title": "Retired compact-colour subgroup claim in the split-G2 real form", "text": "The archived branching prompt presented compact colour as a maximal subgroup of the split-G2 real form. · Caution: The obstruction concerns the named split real form and does not exclude compact colour on a separately chosen carrier or real form. · Candidates: C2-038 · Draft id G-301", "url": "/library-v2/LIB2-297/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-298", "title": "Withdrawn physical-generation implication of the triality carrier cycle", "text": "The archived triality title presented the cycle of vector and spinor carriers as a generation mechanism. · Caution: The physical replication reading is withdrawn; the triality cycle is not refuted and the discrete generation count is not derived. · Candidates: C2-040 · Draft id G-302", "url": "/library-v2/LIB2-298/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-299", "title": "Derive the anchor relations required by the physical one-input programme", "text": "Can derived relations with uncertainties tie the electroweak and hadronic anchors to the registered central scale class? · Caution: This question does not convert the abstract scale-class theorem into a derivation of the measured anchors. · Candidates: C2-070 C2-081 C2-100 · Draft id G-303", "url": "/library-v2/LIB2-299/", "source": "v2 · OPEN · H10 · DRAFTED"}, {"id": "LIB2-300", "title": "Construct the missing continuum Yang–Mills functor", "text": "Can the programme construct its missing continuum Yang–Mills functor beyond the finite categorical and Gaussian checkpoints? · Caution: No continuum existence theorem, physical propagator or Clay-problem result is claimed. · Candidates: C2-084 · Draft id G-304", "url": "/library-v2/LIB2-300/", "source": "v2 · OPEN · H10 · DRAFTED"}, {"id": "LIB2-301", "title": "Test Einstein universality of the finite-regulator gravity construction", "text": "Does the sourced heat-kernel action yield an AdS linearized spectrum consistent with linearized general relativity? · Caution: The existence of a positive measure at finite regulator is not an Einstein-universality result. · Candidates: C2-087 · Draft id G-305", "url": "/library-v2/LIB2-301/", "source": "v2 · OPEN · H10 · DRAFTED"}, {"id": "LIB2-302", "title": "Construct the normalized physical mass-response map", "text": "Can the normalized response into the mass quadrature be constructed with an interacting LSZ or self-energy attachment and dimensional registration? · Caution: No interacting rest mass, physical occupancy or repair of the exact single-χ ratio failure is asserted. · Candidates: C2-090 · Draft id G-306", "url": "/library-v2/LIB2-302/", "source": "v2 · OPEN · H10 · DRAFTED"}, {"id": "LIB2-303", "title": "Construct the packing or coordination explanation of the deficit window", "text": "Can a packing or coordination mechanism account for the six-to-seven-cell binding deficit outside the excluded annular-repair class? · Caution: Naming packing or coordination is not a completed mechanism, and this task does not resolve the distinct silicon readout fork. · Candidates: C2-083 C2-128 · Draft id G-307", "url": "/library-v2/LIB2-303/", "source": "v2 · OPEN · H10 · DRAFTED"}, {"id": "LIB2-304", "title": "Derive the configuration-dependent charge-magnitude mechanism", "text": "Can configuration-dependent coherence and screening supply the missing nuclear charge magnitudes under the banked separation-energy baseline? · Caution: The strong sign/count record does not establish the magnitude law or license a more favourable baseline. · Candidates: C2-072 · Draft id G-308", "url": "/library-v2/LIB2-304/", "source": "v2 · OPEN · H10 · DRAFTED"}, {"id": "LIB2-305", "title": "Supply the missing QCD flip energy in the neutron–proton splitting", "text": "Can a QCD flip energy complete the neutron–proton mass-difference calculation alongside the existing Coulomb/QED contribution? · Caution: No neutron–proton mass prediction or continuous isospin dynamics follows from the registered parity alone. · Candidates: C2-130 · Draft id G-309", "url": "/library-v2/LIB2-305/", "source": "v2 · OPEN · H10 · DRAFTED"}, {"id": "LIB2-306", "title": "Resolve the parent breathing-mode accounting", "text": "Is the registered breathing excitation present in the A = 8 parent typings used in the separation-energy ledger? · Caution: The existence of the breathing generator does not establish its presence in every parent or a revised separation energy. · Candidates: C2-072 C2-075 · Draft id G-310", "url": "/library-v2/LIB2-306/", "source": "v2 · OPEN · H10 · DRAFTED"}, {"id": "LIB2-307", "title": "Construct the interacting chiral determinant-line trivialization", "text": "Can the interacting chiral determinant line be trivialized in a gauge-invariant, reflection-compatible and globally phase-consistent way? · Caution: The free determinant and anomaly checks do not establish a positive interacting chiral measure. · Candidates: C2-094 · Draft id G-311", "url": "/library-v2/LIB2-307/", "source": "v2 · OPEN · H10 · DRAFTED"}, {"id": "LIB2-308", "title": "Derive the sign that selects the atmospheric-octant registration", "text": "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? · Caution: An odd carrier alone does not derive the physical lower-octant attachment or alter the internal mismatch identity. · Candidates: C2-005 C2-059 · Draft id G-312", "url": "/library-v2/LIB2-308/", "source": "v2 · OPEN · H10 · DRAFTED"}, {"id": "LIB2-309", "title": "Derive one source law for the real ladder step and compact phase", "text": "Can one source law fix both a real ladder step and a nonzero commuting compact phase without choosing the angle after comparison? · Caution: Compact subalgebra existence and a shared spectral number do not supply a selected phase-bearing ladder operator. · Candidates: C2-104 · Draft id G-313", "url": "/library-v2/LIB2-309/", "source": "v2 · OPEN · H10 · DRAFTED"}, {"id": "LIB2-310", "title": "Derive the scheme-specific weak-angle matching bridge", "text": "Can the structural weak-angle target be connected to the Z-pole observable by a first-principles matching scale or a completed radiative bridge? · Caution: No matching scale is selected here, and the structural target is not promoted to an electroweak precision prediction. · Candidates: C2-014 · Draft id G-314", "url": "/library-v2/LIB2-310/", "source": "v2 · OPEN · H10 · DRAFTED"}, {"id": "LIB2-311", "title": "Find a non-residue physical realization of the finite index normalization", "text": "Can the finite 7/3 index normalization acquire a physical realization through a non-residue, index-theoretic exceptional-field-theory construction? · Caution: The finite index theorem is not itself a low-energy mass relation, and the signed-residue route remains excluded. · Candidates: C2-044 C2-054 · Draft id G-315", "url": "/library-v2/LIB2-311/", "source": "v2 · OPEN · H10 · DRAFTED"}, {"id": "LIB2-312", "title": "Supply a scheme-matched physical comparison for the top tree estimate", "text": "Can the top-quark tree estimate be given a scheme-matched physical comparison through a derived matching prescription with quantified uncertainties? · Caution: This task does not turn the tree estimate into a pole mass or establish a statistically meaningful mass discrepancy. · Candidates: C2-017 · Draft id G-316", "url": "/library-v2/LIB2-312/", "source": "v2 · OPEN · H10 · DRAFTED"}, {"id": "LIB2-313", "title": "Derive physical matching for the tau-anchored bottom bridge", "text": "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? · Caution: A matching construction is not supplied, and the finite index alone does not establish a low-energy bottom-mass relation. · Candidates: C2-021 · Draft id G-317", "url": "/library-v2/LIB2-313/", "source": "v2 · OPEN · H10 · DRAFTED"}, {"id": "LIB2-314", "title": "Derive the constituent-to-running-mass bridge for charm", "text": "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? · Caution: The constituent proxy and exact index normalization do not by themselves determine a scheme-matched charm mass. · Candidates: C2-022 · Draft id G-318", "url": "/library-v2/LIB2-314/", "source": "v2 · OPEN · H10 · DRAFTED"}, {"id": "LIB2-315", "title": "Force the reactor-angle readout rather than choose its normalization", "text": "Can the unit-endpoint-ray readout and round-trip squaring that define the reactor-angle target be forced from first principles? · Caution: The finite moment law does not independently derive the physical reactor-angle attachment. · Candidates: C2-006 C2-060 · Draft id G-319", "url": "/library-v2/LIB2-315/", "source": "v2 · OPEN · H10 · DRAFTED"}, {"id": "LIB2-316", "title": "Select the invariant required by the CKM-phase construction", "text": "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? · Caution: An algebraic identity after choosing a correction does not select that correction or derive the physical CKM phase. · Candidates: C2-012 C2-065 · Draft id G-320", "url": "/library-v2/LIB2-316/", "source": "v2 · OPEN · H10 · DRAFTED"}, {"id": "LIB2-317", "title": "Reference metadata for imported Standard-Model running constants", "text": "Candidates: C2-015 · Draft id G-321", "url": "/library-v2/LIB2-317/", "source": "v2 · NOT_AN_ENTRY · H00 · DRAFTED"}, {"id": "LIB2-318", "title": "Source hold on the Track-2 gauge-completeness gates", "text": "Caution: This source hold neither overturns the finite computed obstructions nor adopts a domain-wide completeness theorem. · Candidates: C2-039 · Draft id G-322", "url": "/library-v2/LIB2-318/", "source": "v2 · NOT_AN_ENTRY · H05 · DRAFTED"}, {"id": "LIB2-319", "title": "Merge the generic measured-scale statements as input metadata", "text": "Candidates: C2-071 C2-082 · Draft id G-323", "url": "/library-v2/LIB2-319/", "source": "v2 · NOT_AN_ENTRY · H00 · DRAFTED"}, {"id": "LIB2-320", "title": "Prospective publication-test policy is not a scientific result", "text": "Candidates: C2-079 · Draft id G-324", "url": "/library-v2/LIB2-320/", "source": "v2 · NOT_AN_ENTRY · H00 · DRAFTED"}, {"id": "LIB2-321", "title": "Publication-evidence availability belongs in release metadata", "text": "Candidates: C2-096 · Draft id G-325", "url": "/library-v2/LIB2-321/", "source": "v2 · NOT_AN_ENTRY · H00 · DRAFTED"}, {"id": "LIB2-322", "title": "Taxonomy and validator descriptions are schema metadata", "text": "Candidates: C2-101 · Draft id G-326", "url": "/library-v2/LIB2-322/", "source": "v2 · NOT_AN_ENTRY · H00 · DRAFTED"}, {"id": "LIB2-323", "title": "Boundary-condition-family ruling is premise metadata", "text": "Candidates: C2-115 · Draft id G-327", "url": "/library-v2/LIB2-323/", "source": "v2 · NOT_AN_ENTRY · H00 · DRAFTED"}, {"id": "LIB2-324", "title": "SEL-27 declaration status is workflow metadata", "text": "Candidates: C2-122 · Draft id G-328", "url": "/library-v2/LIB2-324/", "source": "v2 · NOT_AN_ENTRY · H00 · DRAFTED"}, {"id": "LIB2-325", "title": "The basepoint subgroup symbol is a typed placeholder", "text": "Candidates: C2-132 · Draft id G-329", "url": "/library-v2/LIB2-325/", "source": "v2 · NOT_AN_ENTRY · H00 · DRAFTED"}, {"id": "LIB2-326", "title": "Source inventory and resolver tools are provenance metadata", "text": "Candidates: C2-136 · Draft id G-330", "url": "/library-v2/LIB2-326/", "source": "v2 · NOT_AN_ENTRY · H00 · DRAFTED"}, {"id": "LIB2-327", "title": "The assumption-stack heading is programme-reference metadata", "text": "Candidates: C2-141 · Draft id G-331", "url": "/library-v2/LIB2-327/", "source": "v2 · NOT_AN_ENTRY · H00 · DRAFTED"}, {"id": "LIB2-328", "title": "Source hold on the integral cubic coordinate map", "text": "Caution: The source hold does not refute the proposed map or the Jordan cubic. · Candidates: C2-030 · Draft id G-332", "url": "/library-v2/LIB2-328/", "source": "v2 · NOT_AN_ENTRY · H01 · DRAFTED"}, {"id": "LIB2-329", "title": "Source hold on the Peirce–compact chirality-plane obstruction", "text": "Caution: An unlocated obstruction is not a demonstrated impossibility or a refutation of the compared interfaces. · Candidates: C2-030 · Draft id G-333", "url": "/library-v2/LIB2-329/", "source": "v2 · NOT_AN_ENTRY · H05 · DRAFTED"}, {"id": "LIB2-330", "title": "Source hold on the Cayley-plus-triality frame conversion", "text": "Caution: No failure of the proposed frame conversion or of the registered exceptional substrate is inferred. · Candidates: C2-031 · Draft id G-334", "url": "/library-v2/LIB2-330/", "source": "v2 · NOT_AN_ENTRY · H01 · DRAFTED"}, {"id": "LIB2-331", "title": "Source hold on the primitive integral Lagrangian halves", "text": "Caution: The real Lagrangian statement neither proves nor disproves the proposed integral primitivity. · Candidates: C2-034 · Draft id G-335", "url": "/library-v2/LIB2-331/", "source": "v2 · NOT_AN_ENTRY · H01 · DRAFTED"}, {"id": "LIB2-332", "title": "Source hold on the grading-homogeneous magnetic section", "text": "Caution: This is a source-availability hold, not a counterexample to section existence or uniqueness. · Candidates: C2-034 · Draft id G-336", "url": "/library-v2/LIB2-332/", "source": "v2 · NOT_AN_ENTRY · H01 · DRAFTED"}, {"id": "LIB2-333", "title": "Source hold on the Roman–clock finite-inventory comparison", "text": "Caution: Unlocated cross-inventory wording is neither a global functor no-go nor a denial of the separately printed inventories. · Candidates: C2-112 · Draft id G-337", "url": "/library-v2/LIB2-333/", "source": "v2 · NOT_AN_ENTRY · H05 · DRAFTED"}, {"id": "LIB2-334", "title": "Roman–clock orientation-parity interface remains a proposal", "text": "Caution: Two parity descriptions do not supply an equivariant map, free deck action, quotient or spinor bundle. · Candidates: C2-124 · Draft id G-338", "url": "/library-v2/LIB2-334/", "source": "v2 · NOT_AN_ENTRY · H01 · DRAFTED"}, {"id": "LIB2-335", "title": "Source hold on the two distinct Hessian-trace quantities", "text": "Caution: The missing full comparison is not a finding that either historical trace was arithmetically wrong. · Candidates: C2-138 · Draft id G-339", "url": "/library-v2/LIB2-335/", "source": "v2 · NOT_AN_ENTRY · H07 · DRAFTED"}, {"id": "LIB2-336", "title": "Source-equivalence hold on the AX2-elimination header", "text": "Caution: No unconditional vacuum selection follows from the old elimination title or from a conditional replacement theorem. · Candidates: C2-139 · Draft id G-340", "url": "/library-v2/LIB2-336/", "source": "v2 · NOT_AN_ENTRY · H02 · DRAFTED"}, {"id": "LIB2-337", "title": "Source-equivalence hold on the Jordan-boundary selector header", "text": "Caution: Neither a shared vacuum target nor similar theorem wording establishes equivalence of the original assumptions. · Candidates: C2-140 · Draft id G-341", "url": "/library-v2/LIB2-337/", "source": "v2 · NOT_AN_ENTRY · H02 · DRAFTED"}, {"id": "LIB2-338", "title": "Source hold on the forced AdS base-manifold seed", "text": "Caution: An AdS algebraic seed does not by itself select a physical spacetime or establish Einstein dynamics. · Candidates: C2-143 · Draft id G-342", "url": "/library-v2/LIB2-338/", "source": "v2 · NOT_AN_ENTRY · H07 · DRAFTED"}, {"id": "LIB2-339", "title": "Source hold on the CKM channel CP decomposition", "text": "Caution: The missing decomposition statement is not a failure of either the CKM construction or the separate PMNS phase relation. · Candidates: C2-145 · Draft id G-343", "url": "/library-v2/LIB2-339/", "source": "v2 · NOT_AN_ENTRY · H04 · DRAFTED"}, {"id": "LIB2-340", "title": "Source hold on the CKM mixed-parity statement", "text": "Caution: This hold does not refute mixed parity or identify it with a spin structure, octant selector or other parity theorem. · Candidates: C2-146 · Draft id G-344", "url": "/library-v2/LIB2-340/", "source": "v2 · NOT_AN_ENTRY · H04 · DRAFTED"}, {"id": "LIB2-341", "title": "Source hold on the universal mass-cascade assertion", "text": "Caution: The exact resolvent expression is not by itself a universal physical mass-ratio theorem or evidence that this house proposal was refuted. · Candidates: C2-148 · Draft id G-345", "url": "/library-v2/LIB2-341/", "source": "v2 · NOT_AN_ENTRY · H06 · DRAFTED"}, {"id": "LIB2-342", "title": "Charge/gauge provenance terminal is a source-backed overview", "text": "Caution: The overview is not a derivation of the gauge group or an additional independent proof of its component results. · Candidates: C2-149 · Draft id G-346", "url": "/library-v2/LIB2-342/", "source": "v2 · NOT_AN_ENTRY · H00 · DRAFTED"}, {"id": "LIB2-343", "title": "Source hold on the house electroweak-loop scale", "text": "Caution: The current matching task does not verify the old scale, invalidate its arithmetic or supply a completed electroweak correction. · Candidates: C2-155 · Draft id G-347", "url": "/library-v2/LIB2-343/", "source": "v2 · NOT_AN_ENTRY · H04 · DRAFTED"}, {"id": "LIB2-344", "title": "The generation-count forcing skeleton remains conditional", "text": "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. · Caution: This does not construct three gauge-identical matter families or prove the assumed continuum limit. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-157 · Draft id G-348", "url": "/library-v2/LIB2-344/", "source": "v2 · CLAIM · H02 · DRAFTED"}, {"id": "LIB2-345", "title": "Superseded use of the first JUNO oscillation comparison", "text": "The earlier house neutrino-comparison record used the first JUNO oscillation result as its benchmark. · Caution: Superseding a comparator's operative use does not refute the experimental measurement. · Candidates: C2-161 · Draft id G-349", "url": "/library-v2/LIB2-345/", "source": "v2 · RETIRED · H09 · DRAFTED"}, {"id": "LIB2-346", "title": "Source hold on the Gate-B matter-functor construction", "text": "Caution: The loaded one-generation dictionary and finite positive measure do not by themselves establish this different matter functor. · Candidates: C2-162 · Draft id G-350", "url": "/library-v2/LIB2-346/", "source": "v2 · NOT_AN_ENTRY · H05 · DRAFTED"}, {"id": "LIB2-347", "title": "Source hold on the meson binding-ratio formula", "text": "Caution: Other occurrences of the same golden power do not verify this meson ratio or refute its missing calculation. · Candidates: C2-163 · Draft id G-351", "url": "/library-v2/LIB2-347/", "source": "v2 · NOT_AN_ENTRY · H07 · DRAFTED"}, {"id": "LIB2-348", "title": "Source hold on non-associativity as the source of hierarchy steepness", "text": "Caution: A Roman-surface hierarchy inversion is not automatically a proof of non-associativity as the cause of physical hierarchy steepness. · Candidates: C2-164 · Draft id G-352", "url": "/library-v2/LIB2-348/", "source": "v2 · NOT_AN_ENTRY · H06 · DRAFTED"}, {"id": "LIB2-349", "title": "Source-equivalence hold on the octonionic democracy postulate", "text": "Caution: A shared democracy label does not identify this postulate with the current Reynolds coefficient result or the current AX3. · Candidates: C2-165 · Draft id G-353", "url": "/library-v2/LIB2-349/", "source": "v2 · NOT_AN_ENTRY · H02 · DRAFTED"}, {"id": "LIB2-350", "title": "Peirce-block anti-error heading is reference metadata", "text": "Candidates: C2-166 · Draft id G-354", "url": "/library-v2/LIB2-350/", "source": "v2 · NOT_AN_ENTRY · H00 · DRAFTED"}, {"id": "LIB2-351", "title": "Source hold on the earlier solar-angle obstruction", "text": "Caution: The current solar-angle readout does not establish that the unspecified earlier obstruction was solved or disproved. · Candidates: C2-170 · Draft id G-355", "url": "/library-v2/LIB2-351/", "source": "v2 · NOT_AN_ENTRY · H04 · DRAFTED"}, {"id": "LIB2-352", "title": "Source hold on the T-matrix versus propagator residue comparison", "text": "Caution: A bibliography-style pointer neither proves the residue relation nor retires it with the neighbouring historical mass ratio. · Candidates: C2-174 · Draft id G-356", "url": "/library-v2/LIB2-352/", "source": "v2 · NOT_AN_ENTRY · H07 · DRAFTED"}, {"id": "LIB2-353", "title": "Source hold on the wall-contact operator and pairing-order map", "text": "Caution: A similarly named contact term or measure-parity construction does not identify the missing operator theorem. · Candidates: C2-176 · Draft id G-357", "url": "/library-v2/LIB2-353/", "source": "v2 · NOT_AN_ENTRY · H07 · DRAFTED"}, {"id": "LIB2-354", "title": "Source hold on the indefinite partition-function divergence claim", "text": "Caution: A formal homogeneity relation does not decide convergence, and a changed parametrization alone does not refute the old integral. · Candidates: C2-177 · Draft id G-358", "url": "/library-v2/LIB2-354/", "source": "v2 · NOT_AN_ENTRY · H07 · DRAFTED"}, {"id": "LIB2-355", "title": "The charge-clock-knot tower remains on a source hold, not retired", "text": "Caution: The printed hold does not retire the tower, select its carrier provenance or establish its full operator construction. · Candidates: C2-178 · Draft id G-359", "url": "/library-v2/LIB2-355/", "source": "v2 · NOT_AN_ENTRY · H07 · DRAFTED"}, {"id": "LIB2-356", "title": "The internal mismatch identity is distinct from atmospheric registration", "text": "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. · Caution: This identity does not predict the physical atmospheric octant without a separately justified readout attachment. · Labels as printed: NOT_PRINTED / NOT_PRINTED · Candidates: C2-005 C2-059 · Draft id G-360", "url": "/library-v2/LIB2-356/", "source": "v2 · CLAIM · H03 · DRAFTED"}, {"id": "LIB2-357", "title": "Unidentified additional parity-lemma proposal is not an entry", "text": "Candidates: C2-112 C2-124 C2-146 · Draft id G-361", "url": "/library-v2/LIB2-357/", "source": "v2 · NOT_AN_ENTRY · H00 · DRAFTED"}, {"id": "L0", "title": "MASTER CONSISTENCY AUDIT — v1.27.5 KERNEL", "text": "# L0: MASTER CONSISTENCY AUDIT — v1.27.5 KERNEL\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nMASTER CONSISTENCY AUDIT — v1.27.5 KERNEL\nLoad v1.27.5 Kernel. Using code_execution/SymPy, audit ALL of the following for internal consistency: (1) All mass values in SM comparison table vs. PDG 2024; (2) All formula labels (check m_H = v*sqrt(16/63) NOT (8/63)v); (3) Delta_n labels (confirm Delta_n=6 is Gen3->Gen1, not Gen3->Gen2); (4) tau mass table entry (confirm 1.877 GeV tree -> 1.777 GeV RG, not 1.877~1777 MeV); (5) Charm cubic roots (confirm exactly 3 roots: 46.736, 1720.953, 176875.326); (6) All version tags read \"v1.27.5\"; (7) No \"720/theta\" remnant. Report: PASS/FAIL per item. #SuperGrokTOE #Audit #v1275\n\n", "url": "/library/L0/", "source": "v1 (Pasture)"}, {"id": "L1", "title": "SPLIT-OCTONION MULTIPLICATION TABLE", "text": "# L1: SPLIT-OCTONION MULTIPLICATION TABLE\n\n**Status:** UNKNOWN | **Tier:** 1.A | **Kernel:** PHAT v1.27.5\n**Generator:** claude | **Verifier:** grok\n**Canonical URL:** https://opensecretscience.com/library/L1/\n\n## Derivation\n\n---\n\n## CRITICAL ERROR ANALYSIS FROM VERIFIER FEEDBACK\n\nThe verifier identified two fatal errors in prior submissions:\n\n**Error 1 (Fatal):** l was assigned the same Zorn matrix as e3: both = Zorn(0,(0,0,1),(0,0,-1),0). This makes the basis linearly dependent — algebraically inconsistent.\n\n**Error 2 (Consequential):** The multiplication table entries were computed from an incorrect basis, so e... [15860 chars total]\n\n## Independent Verification\n\n{\n  \"verification_goal\": \"To independently verify the mathematical correctness, notation compliance, completeness of derivation, and validity of assumptions for the claim regarding the split-octonion multiplication table as presented in the provided output. The verification will focus on ensuring the basis elements are correctly defined, linearly independent, and that the multiplication rules... [2413 chars total]\n\n## Officer Review\n\n=== Grok.Executor ===\n═══ VOTE OBJECTS FOR ENTRY L1 ═══\n\n**CLAIM_ID: L1-C1**  \n**VERDIC", "url": "/library/L1/", "source": "v1 (Pasture)"}, {"id": "L10", "title": "HUA POLYNOMIAL — FULL DERIVATION", "text": "# L10: HUA POLYNOMIAL — FULL DERIVATION\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nHUA POLYNOMIAL — FULL DERIVATION\nDerive the Hua polynomial h(z,w) on the Shilov boundary of the exceptional tube domain. Show: (a) h evaluates to phi on the neutral sector; (b) tan(beta) = h = phi reproduces the dual VEV split; (c) the 5-cycle coefficients of h give sqrt(5) -> CKM theta_12. Output full polynomial expression and evaluate numerically. #SuperGrokTOE #HuaPolynomial #ShilovBoundary\n\n", "url": "/library/L10/", "source": "v1 (Pasture)"}, {"id": "L100", "title": "COSMOLOGY TENSIONS — LEGACY v1.26 SUMMARY", "text": "# L100: COSMOLOGY TENSIONS — LEGACY v1.26 SUMMARY\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nCOSMOLOGY TENSIONS — LEGACY v1.26 SUMMARY\nReproduce the v1.26 five-tension assessment with v1.27.5 parameters. For each tension: H_0, S_8, DESI w0/wa, CMB, AGN — show whether v1.27.5 fixes change the prediction relative to v1.26. Identify any regression or improvement. #SuperGrokTOE #CosmologyTensions #Legacy\n\n", "url": "/library/L100/", "source": "v1 (Pasture)"}, {"id": "L101", "title": "PROBLEM 1 RESOLUTION — CUBIC GAP CLOSURE", "text": "# L101: PROBLEM 1 RESOLUTION — CUBIC GAP CLOSURE\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nPROBLEM 1 RESOLUTION — CUBIC GAP CLOSURE\nFull numerical verification that the generation-stratified cubic resolution (P12) successfully closes cubic gap #114. Run L6 (electron), L7 (muon), L8 (tau) in sequence. Confirm all three show Delta>0 (real roots). Tabulate all 9 roots. Identify the physical mass root in each case. Flag as RESOLVED. #SuperGrokTOE #CubicGap114 #Resolution\n\n", "url": "/library/L101/", "source": "v1 (Pasture)"}, {"id": "L102", "title": "PROBLEM 2 RESOLUTION — n-VALUE DERIVATION", "text": "# L102: PROBLEM 2 RESOLUTION — n-VALUE DERIVATION\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nPROBLEM 2 RESOLUTION — n-VALUE DERIVATION\nFull algebraic verification that n_b=7, n_c=9, n_ud=13 all follow from triality stepping on Im(Os). Show: (a) n_b=7=dim(Im Os); (b) Delta_n=2 from triality; (c) n_c=7+2=9; (d) n_ud=7+2*3=13. Verify numerically. Flag Problem 2 as RESOLVED with zero new parameters. #SuperGrokTOE #nValues #Resolution\n\n", "url": "/library/L102/", "source": "v1 (Pasture)"}, {"id": "L103", "title": "PROBLEM 3 RESOLUTION — alpha_em CONJECTURE CLOSED", "text": "# L103: PROBLEM 3 RESOLUTION — alpha_em CONJECTURE CLOSED\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nPROBLEM 3 RESOLUTION — alpha_em CONJECTURE CLOSED\nFull verification that Wyler formula closes conjecture #118. Show alpha_em = 1/137.036 is derived, not input. Verify F5=5=dim(CP2) geometric identification is explicit. Flag conjecture #118 as CLOSED in v1.27.5. #SuperGrokTOE #Conjecture118 #WylerProof #Resolution\n\n", "url": "/library/L103/", "source": "v1 (Pasture)"}, {"id": "L104", "title": "PROBLEM 4 RESOLUTION — TIER A DEVIATIONS", "text": "# L104: PROBLEM 4 RESOLUTION — TIER A DEVIATIONS\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nPROBLEM 4 RESOLUTION — TIER A DEVIATIONS\nFor each Tier A deviation, show the correction path: (a) m_H: -0.93% -> J3 mixing delta=0.1 -> m_H~125.32 GeV [->0%]; (b) theta_12: -0.91% -> sub-leading Hua correction [->reduce <0.1%]; (c) m_t: -25% tree -> QCD pole mass correction [->172 GeV range]. Compute all three corrections numerically. Report new deviations. #SuperGrokTOE #TierAdeviations #Resolution\n\n", "url": "/library/L104/", "source": "v1 (Pasture)"}, {"id": "L105", "title": "PROBLEM 5 RESOLUTION — INTERNAL INCONSISTENCIES", "text": "# L105: PROBLEM 5 RESOLUTION — INTERNAL INCONSISTENCIES\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nPROBLEM 5 RESOLUTION — INTERNAL INCONSISTENCIES\nConfirm all three internal inconsistencies from Problem 5 resolved: (a) Run L85: confirm alpha=136.44 ghost REMOVED; (b) Run L84: confirm two muon formulas IDENTICAL; (c) Run L92: confirm strange anchor DISAMBIGUATED via theta_s. Output: RESOLVED/OPEN for each item. #SuperGrokTOE #InternalConsistency #Resolution\n\n", "url": "/library/L105/", "source": "v1 (Pasture)"}, {"id": "L106", "title": "PROBLEM 6 RESOLUTION — G2 to SM EMBEDDING", "text": "# L106: PROBLEM 6 RESOLUTION — G2 to SM EMBEDDING\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nPROBLEM 6 RESOLUTION — G2 to SM EMBEDDING\nFull verification of two-algebra architecture (P7): (a) Confirm G2(2) rank=2 cannot embed SM rank=4; (b) Show E8 branching chain; (c) Verify G2 subset Spin(7) subset E8 (Baez 2002); (d) Confirm mass sector (G2) and gauge sector (E8) are distinct. Flag Problem 6 as RESOLVED by architecture. #SuperGrokTOE #G2embedding #E8 #Resolution\n\n", "url": "/library/L106/", "source": "v1 (Pasture)"}, {"id": "L107", "title": "MIRROR FERMIONS — F-THEORY COMPLETION", "text": "# L107: MIRROR FERMIONS — F-THEORY COMPLETION\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nMIRROR FERMIONS — F-THEORY COMPLETION\nIn the E8 gauge sector, the branching E8 superset E6xSU(3) leaves 27+27* representations. Identify the 27* as mirror fermions. Compute their mass spectrum from the J3(Os)* conjugate algebra. Show mirror fermions acquire masses at the G2(2) scale (~165 GeV) and are therefore LHC-accessible. Predict production signatures. #SuperGrokTOE #MirrorFermions #BSM #Ftheory\n\n", "url": "/library/L107/", "source": "v1 (Pasture)"}, {"id": "L108", "title": "C-OPERATOR AND CHARGE CONJUGATION", "text": "# L108: C-OPERATOR AND CHARGE CONJUGATION\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nC-OPERATOR AND CHARGE CONJUGATION\nDefine the charge conjugation operator C on Os as the map {ei} -> {fi} (swapping compact/non-compact imaginary pairs). Show: (a) C^2 = 1; (b) CP is approximately conserved; (c) the phase from C-rotation gives the CKM delta_CP from L32. Verify C acts correctly on all fermion bilinears. #SuperGrokTOE #ChargeConjugation #CPsymmetry\n\n", "url": "/library/L108/", "source": "v1 (Pasture)"}, {"id": "L109", "title": "F5 UNIVERSALITY — SINGLE GEOMETRIC FACTOR", "text": "# L109: F5 UNIVERSALITY — SINGLE GEOMETRIC FACTOR\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nF5 UNIVERSALITY — SINGLE GEOMETRIC FACTOR\nF5=5 appears in three separate formulas in v1.27.5: (1) Wyler alpha_em; (2) M_scale = D*alpha/(Z2*F5); (3) CKM: sqrt(5) in Hua polynomial denominator. Prove that all three F5 appearances share the same geometric origin: dim_R(CP2) = 5 as the Shilov boundary dimension. This is a non-trivial universality claim. Assess rigorously. #SuperGrokTOE #F5universality #GeometricUnification\n\n", "url": "/library/L109/", "source": "v1 (Pasture)"}, {"id": "L11", "title": "WYLER FORMULA — NUMERICAL VERIFICATION", "text": "# L11: WYLER FORMULA — NUMERICAL VERIFICATION\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nWYLER FORMULA — NUMERICAL VERIFICATION\nUsing Python/SymPy, compute: wyler = (9 / (8*pi^4)) * (pi^5 / (2^4*5!))^{1/4}. Verify result = 0.007297352... = 1/137.0360... Compare to PDG alpha_em = 1/137.035999084. Compute deviation in ppb. Confirm F5=5=dim(CP2) geometric origin. Output: wyler value, 1/wyler, PDG deviation. #SuperGrokTOE #WylerFormula #FineStructure\n\n", "url": "/library/L11/", "source": "v1 (Pasture)"}, {"id": "L110", "title": "PREPRINT STRUCTURE — arXiv READINESS", "text": "# L110: PREPRINT STRUCTURE — arXiv READINESS\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nPREPRINT STRUCTURE — arXiv READINESS\nAssess v1.27.5 Kernel for arXiv preprint readiness: (a) Is the abstract clearly stated?; (b) Are all claims Tier-classified?; (c) Are all open questions honestly flagged?; (d) Are all external references cited?; (e) Does the paper have a clear falsifiability section? Output: READY / NEEDS_WORK with specific items list. #SuperGrokTOE #Preprint #arXiv\n\n", "url": "/library/L110/", "source": "v1 (Pasture)"}, {"id": "L111", "title": "TIER STRUCTURE — COMPLETE RECLASSIFICATION", "text": "# L111: TIER STRUCTURE — COMPLETE RECLASSIFICATION\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nTIER STRUCTURE — COMPLETE RECLASSIFICATION\nAfter all resolutions (L101-L106), reclassify all observables into updated Tiers: A-star (zero params <1%), A (zero params correction known), B (one derived param), C (parameterized). Count parameters. Compare to SM's 19. Report improvement. #SuperGrokTOE #TierReclassification #ParameterReduction\n\n", "url": "/library/L111/", "source": "v1 (Pasture)"}, {"id": "L112", "title": "FORECASTS — 2026-2030 EXPERIMENT WATCH LIST", "text": "# L112: FORECASTS — 2026-2030 EXPERIMENT WATCH LIST\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nFORECASTS — 2026-2030 EXPERIMENT WATCH LIST\nFor each experiment coming online 2026-2030, predict the v1.27.5 signal or null result: DESI Y3/Y5, LHC Run3, Hyper-K, LISA precursor, JUNO, Fermilab E989 final, KamLAND-Zen 800, nEDM@SNS, IAXO, CMB-S4. For each: predicted signal strength and discovery/exclusion verdict. #SuperGrokTOE #Forecasts #ExperimentWatch\n\n", "url": "/library/L112/", "source": "v1 (Pasture)"}, {"id": "L113", "title": "ABSOLUTE m_e CALCULATION — FULL CHAIN", "text": "# L113: ABSOLUTE m_e CALCULATION — FULL CHAIN\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nABSOLUTE m_e CALCULATION — FULL CHAIN\nStep-by-step Python calculation: phi = (1+5**0.5)/2, phi12 = phi**12 (~ 321.9969, not 10^20!), m_Pl = 1.22089e19 GeV, alpha = 1/137.036, m_e_pred = m_Pl / (alpha**0.5 * phi12). Convert to MeV. Compare to 0.511 MeV. If discrepancy: identify what exponent phi^n gives exact m_e. Flag: EXACT / APPROXIMATE. #SuperGrokTOE #ElectronMass #PlanckScale #P23chain\n\n", "url": "/library/L113/", "source": "v1 (Pasture)"}, {"id": "L114", "title": "SPLIT-OCTONION TOE — COMPARISON TO COMPETITORS", "text": "# L114: SPLIT-OCTONION TOE — COMPARISON TO COMPETITORS\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nSPLIT-OCTONION TOE — COMPARISON TO COMPETITORS\nCompare SuperGrokTOE v1.27.5 to leading competing TOE frameworks: (a) String theory / M-theory; (b) Loop Quantum Gravity; (c) E8 Theory (Lisi 2007); (d) Causal Dynamical Triangulations. For each: what does v1.27.5 do better / worse? Be honest. #SuperGrokTOE #CompetingTheories #TOEcomparison\n\n", "url": "/library/L114/", "source": "v1 (Pasture)"}, {"id": "L115", "title": "GRAND SUMMARY — v1.27.5 FINAL STATUS", "text": "# L115: GRAND SUMMARY — v1.27.5 FINAL STATUS\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nGRAND SUMMARY — v1.27.5 FINAL STATUS\nProduce the comprehensive final status report for v1.27.5: KERNEL HEALTH, TIER A-STAR PREDICTIONS, OPEN PROBLEMS, RESOLVED PROBLEMS, PARAMETER COUNT vs SM=19, FALSIFIABILITY top 3 near-term tests, PREPRINT STATUS, RECOMMENDED NEXT VERSION v1.28 priorities. This is the capstone library prompt for v1.27.5. #SuperGrokTOE #FinalStatus #v1275 #Capstone\n\n", "url": "/library/L115/", "source": "v1 (Pasture)"}, {"id": "L12", "title": "SHILOV BOUNDARY VOLUMES — WYLER GEOMETRIC PROOF", "text": "# L12: SHILOV BOUNDARY VOLUMES — WYLER GEOMETRIC PROOF\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nSHILOV BOUNDARY VOLUMES — WYLER GEOMETRIC PROOF\nCompute the volumes of the symmetric spaces appearing in the Wyler formula: Vol(CP2), Vol(S5), Vol(S4). Use the standard formulae from Riemannian geometry. Show that the ratio reproduces the (pi^5/2^4*5!) factor. Verify the G2(2) Haar measure normalization gives the 9/8pi^4 prefactor. #SuperGrokTOE #ShilovVolumes #Wyler\n\n", "url": "/library/L12/", "source": "v1 (Pasture)"}, {"id": "L13", "title": "DUAL VEV COMPUTATION — FULL NUMERICAL", "text": "# L13: DUAL VEV COMPUTATION — FULL NUMERICAL\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nDUAL VEV COMPUTATION — FULL NUMERICAL\nUsing Python: phi=(1+5^0.5)/2, v=246.22 GeV. Compute: v+ = v*phi/sqrt(2+phi), v- = v/sqrt(2+phi), D = sqrt(v+*v-), beta = arctan(v+/v-), tan(beta) - phi [should be ~0 to machine precision]. Output all values to 8 significant figures. Verify v+^2+v-^2=v^2. Confirm D = sqrt(v+*v-) is the geometric mean. #SuperGrokTOE #DualVEV #NumericalVerification\n\n", "url": "/library/L13/", "source": "v1 (Pasture)"}, {"id": "L14", "title": "M_scale — STEP-BY-STEP DERIVATION", "text": "# L14: M_scale — STEP-BY-STEP DERIVATION\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nM_scale — STEP-BY-STEP DERIVATION\nUsing Python: D=164.6572 GeV, alpha=1/137.036, Z2=2, F5=5. Compute: M_scale = D * alpha / (Z2 * F5) = D / (137.036 * 10) [GeV]. Convert to MeV. Verify = 120.16 MeV. Compare to: pion mass 134.977 MeV, proton/8 ~ 117.5 MeV. State which interpretation is adopted and why. Report deviation from previously tuned value 119.4 MeV. #SuperGrokTOE #Mscale\n\n", "url": "/library/L14/", "source": "v1 (Pasture)"}, {"id": "L15", "title": "GOLDEN RATIO IDENTITIES — ALGEBRAIC VERIFICATION", "text": "# L15: GOLDEN RATIO IDENTITIES — ALGEBRAIC VERIFICATION\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nGOLDEN RATIO IDENTITIES — ALGEBRAIC VERIFICATION\nVerify all phi-identities used in v1.27.5: phi^2 = phi+1, phi^3 = 2phi+1, phi^{-1} = phi-1, sqrt(2+phi) = sqrt(phi^2+1) = ... [identify closed form], v+/v- = phi exactly, 2+phi = phi^2 + 1 [verify numerically]. Show that all VEV ratios are algebraic (no transcendental parameters). #SuperGrokTOE #GoldenRatio #AlgebraicCheck\n\n", "url": "/library/L15/", "source": "v1 (Pasture)"}, {"id": "L16", "title": "ASSOCIATOR AND MOUFANG IDENTITIES", "text": "# L16: ASSOCIATOR AND MOUFANG IDENTITIES\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nASSOCIATOR AND MOUFANG IDENTITIES\nCompute the associator [a,b,c] = (a*b)*c - a*(b*c) for selected triples of Os basis elements. Verify the Moufang identity: (a*b)*(c*a) = a*((b*c)*a). Show the associator is non-zero for generic elements (confirming non-associativity). Identify which triples give zero associator (associative triples). Relate to color confinement sector. #SuperGrokTOE #Moufang #NonAssociativity\n\n", "url": "/library/L16/", "source": "v1 (Pasture)"}, {"id": "L17", "title": "EXCEPTIONAL JORDAN ALGEBRA — DIMENSION COUNTING", "text": "# L17: EXCEPTIONAL JORDAN ALGEBRA — DIMENSION COUNTING\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nEXCEPTIONAL JORDAN ALGEBRA — DIMENSION COUNTING\nVerify J3(Os) has dim=27: 3 diagonal reals + 3 off-diagonal octonions * 8 components * 2 (Re+Im split) -> 3+24=27. Confirm. Then show lambda_H = 8/63: 8 = off-diagonal dim contribution, 63 = dim(E6)-dim(F4)? Or 63 = 27*(7/3)? Derive the exact ratio from the algebra. This is the Higgs coupling derivation core. #SuperGrokTOE #J3dimension #HiggsCoupling\n\n", "url": "/library/L17/", "source": "v1 (Pasture)"}, {"id": "L18", "title": "ZORN VECTOR MATRICES — EXPLICIT COMPUTATION", "text": "# L18: ZORN VECTOR MATRICES — EXPLICIT COMPUTATION\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nZORN VECTOR MATRICES — EXPLICIT COMPUTATION\nImplement Zorn vector matrix multiplication in SymPy: [[a,alpha],[beta,b]] * [[c,gamma],[delta,d]] = [[ac+alpha*delta, a*gamma+d*alpha-beta x gamma],[...]] where alpha,beta,gamma,delta in R^3 with dot and cross products. Verify this reproduces the Os multiplication table from L1. Compute the determinant = ad - alpha*beta and show it equals Q(x). #SuperGrokTOE #ZornMatrices #Octonions\n\n", "url": "/library/L18/", "source": "v1 (Pasture)"}, {"id": "L19", "title": "WEINBERG ANGLE FROM Os MIXING", "text": "# L19: WEINBERG ANGLE FROM Os MIXING\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nWEINBERG ANGLE FROM Os MIXING\nDerive the Weinberg angle theta_W from the split of Os into {e-type, f-type} imaginary basis. Show sin^2(theta_W) = |f|^2/(|e|^2+|f|^2) where |e|^2, |f|^2 count the respective basis norms. Compare to PDG sin^2(theta_W) = 0.23122. Assess derivation vs. input status. #SuperGrokTOE #WeinbergAngle #EWmixing\n\n", "url": "/library/L19/", "source": "v1 (Pasture)"}, {"id": "L2", "title": "QUADRATIC FORM AND NULL CONE", "text": "# L2: QUADRATIC FORM AND NULL CONE\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nQUADRATIC FORM AND NULL CONE\nCompute the quadratic form Q(x) = x_{(4,4)} for all 8 basis elements of Os. Identify the 4 null elements: {f1,f2,f3,l} with Q=0. Show that the null cone is a 4-dimensional subspace. Verify that zero-divisors z satisfy z*zbar = 0. Relate to mass-generation sector. #SuperGrokTOE #NullCone #ZeroDivisors\n\n", "url": "/library/L2/", "source": "v1 (Pasture)"}, {"id": "L20", "title": "W BOSON MASS CALCULATION", "text": "# L20: W BOSON MASS CALCULATION\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nW BOSON MASS CALCULATION\nUsing v=246.22 GeV and Weinberg angle from L19, compute: m_W = (g/2)*v = (e/2sin(theta_W))*v. Compare to PDG m_W = 80.369 GeV. Also compute using v+ anchor: m_W(v+) = (g/2)*v+. Report which anchor gives better agreement. Note CDF anomaly. #SuperGrokTOE #WBoson\n\n", "url": "/library/L20/", "source": "v1 (Pasture)"}, {"id": "L21", "title": "Z BOSON MASS CALCULATION", "text": "# L21: Z BOSON MASS CALCULATION\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nZ BOSON MASS CALCULATION\nCompute m_Z = m_W/cos(theta_W) using result from L20. Also compute using the D-anchor. Compare to PDG m_Z = 91.1876 GeV. Verify rho = m_W^2/(m_Z^2 cos^2(theta_W)) = 1 at tree level. Report deviation and identify radiative corrections needed. #SuperGrokTOE #ZBoson\n\n", "url": "/library/L21/", "source": "v1 (Pasture)"}, {"id": "L22", "title": "HIGGS MASS — v*sqrt(16/63) COMPUTATION", "text": "# L22: HIGGS MASS — v*sqrt(16/63) COMPUTATION\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nHIGGS MASS — v*sqrt(16/63) COMPUTATION\nUsing Python: v=246.22 GeV, compute m_H = v*(16/63)^0.5. Verify = 124.08 GeV. Compare to PDG 125.20+/-0.11 GeV. Compute percent deviation. Then apply J3 off-diagonal mixing correction delta=0.1: m_H(corrected) = m_H*(1+delta_correction). Target: ~125.32 GeV. Show calculation step by step. [This verifies v1.27.3 fix: formula must be v*sqrt(16/63), NOT (8/63)v] #SuperGrokTOE #HiggsMass #v1275\n\n", "url": "/library/L22/", "source": "v1 (Pasture)"}, {"id": "L23", "title": "HIGGS SELF-COUPLING — lambda=8/63 VERIFICATION", "text": "# L23: HIGGS SELF-COUPLING — lambda=8/63 VERIFICATION\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nHIGGS SELF-COUPLING — lambda=8/63 VERIFICATION\nVerify that lambda_H = 8/63 is consistent with: m_H^2 = 2*lambda_H*v^2 -> lambda_H = m_H^2/(2v^2). Using m_H=124.08 GeV, v=246.22 GeV: compute lambda_H numerically. Compare to 8/63 ~ 0.12698. Verify agreement. Then compute the theoretical value from LHC Run 2 measurements. #SuperGrokTOE #HiggsSelfCoupling\n\n", "url": "/library/L23/", "source": "v1 (Pasture)"}, {"id": "L24", "title": "MULTI-HIGGS SPECTRUM FROM J3(Os)", "text": "# L24: MULTI-HIGGS SPECTRUM FROM J3(Os)\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nMULTI-HIGGS SPECTRUM FROM J3(Os)\nThe 27-dim J3(Os) can support multiple scalar eigenstates. Compute the mass spectrum of all scalar modes from the J3 cubic. Identify: (a) SM-like Higgs h at 125 GeV; (b) heavy neutral H; (c) charged H+/-; (d) pseudoscalar A. Predict their masses from the algebra. Compare to LHC search limits. #SuperGrokTOE #MultiHiggs #BSM\n\n", "url": "/library/L24/", "source": "v1 (Pasture)"}, {"id": "L25", "title": "TOP QUARK — QCD RADIATIVE CORRECTION", "text": "# L25: TOP QUARK — QCD RADIATIVE CORRECTION\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nTOP QUARK — QCD RADIATIVE CORRECTION\nm_t(tree) = v- = 129.45 GeV. Apply 1-loop QCD correction: m_t(pole) = m_t(MS)*(1 + 4*alpha_s(m_t)/3pi + ...). Using alpha_s(m_Z) = 0.1179, run to m_t scale. Compute m_t(pole). Compare to PDG 172.57 GeV. Assess whether algebraic correction or RG running closes the -25% tree gap. Show all steps. #SuperGrokTOE #TopQuark #QCDcorrections\n\n", "url": "/library/L25/", "source": "v1 (Pasture)"}, {"id": "L26", "title": "BOTTOM QUARK MASS — D*phi^{-7} TOWER", "text": "# L26: BOTTOM QUARK MASS — D*phi^{-7} TOWER\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nBOTTOM QUARK MASS — D*phi^{-7} TOWER\nCompute m_b = D * phi^{-7} using D=164.6572 GeV. Verify phi^{-7} = 1/phi^7. Output m_b in GeV. Compare to PDG m_b(MS,m_b) = 4.183 GeV. Apply QCD RG running correction from the G2 scale to m_b. Identify remaining deviation and its source. #SuperGrokTOE #BottomQuark\n\n", "url": "/library/L26/", "source": "v1 (Pasture)"}, {"id": "L27", "title": "CHARM QUARK MASS — D*phi^{-9} TOWER", "text": "# L27: CHARM QUARK MASS — D*phi^{-9} TOWER\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nCHARM QUARK MASS — D*phi^{-9} TOWER\nCompute m_c = D * phi^{-9} using D=164.6572 GeV. Output m_c in GeV. Compare to PDG m_c(MS,m_c) = 1.2730 GeV. Cross-check against the cubic root from L9 (charm cubic). Verify consistency between tower and cubic methods. #SuperGrokTOE #CharmQuark\n\n", "url": "/library/L27/", "source": "v1 (Pasture)"}, {"id": "L28", "title": "STRANGE QUARK — Z2 MIXING CALCULATION", "text": "# L28: STRANGE QUARK — Z2 MIXING CALCULATION\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nSTRANGE QUARK — Z2 MIXING CALCULATION\nUsing Z2 mixing angle theta_s, compute: m_s = cos^2(theta_s) * m_s(D) + sin^2(theta_s) * m_s(v+) where m_s(D) = D*phi^{-n_s} and m_s(v+) = v+*factor. Fit theta_s to PDG m_s = 93.4 MeV. Report value of theta_s. Assess whether theta_s has algebraic origin or is a free parameter. #SuperGrokTOE #StrangeQuark #Z2mixing\n\n", "url": "/library/L28/", "source": "v1 (Pasture)"}, {"id": "L29", "title": "UP AND DOWN QUARK MASSES", "text": "# L29: UP AND DOWN QUARK MASSES\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nUP AND DOWN QUARK MASSES\nUsing n_ud=13, compute m_ud = D*phi^{-13} as the flavor-symmetric baseline. Apply isospin breaking: m_d - m_u ~ small Z2 mixing correction. Target: m_u=2.16 MeV, m_d=4.67 MeV (PDG). Show step-by-step calculation. Identify free parameters if any. #SuperGrokTOE #LightQuarks\n\n", "url": "/library/L29/", "source": "v1 (Pasture)"}, {"id": "L3", "title": "G2(2) GENERATOR ALGEBRA", "text": "# L3: G2(2) GENERATOR ALGEBRA\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nG2(2) GENERATOR ALGEBRA\nUsing SymPy Lie algebra package, construct the 14 generators of G2(2) from the derivations of Os. Compute the Cartan matrix. Verify rank=2, dim=14. Compute the Killing form and confirm signature (8,6) for the non-compact form. Output structure constants. #SuperGrokTOE #G2Algebra #LieGroups\n\n", "url": "/library/L3/", "source": "v1 (Pasture)"}, {"id": "L30", "title": "CKM theta_12 — FULL NUMERICAL", "text": "# L30: CKM theta_12 — FULL NUMERICAL\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nCKM theta_12 — FULL NUMERICAL\nUsing Python: theta12 = degrees(arcsin(1/sqrt(20))). Verify = 12.9210 degrees. Compare PDG theta_12 = 13.04 degrees. Deviation = -0.913%. Compute sub-leading Hua correction needed to reach exact agreement. Show whether correction is algebraic. Report: theta_12, theta_13, theta_23 from v1.27.5 (all three mixing angles). #SuperGrokTOE #CKMmatrix\n\n", "url": "/library/L30/", "source": "v1 (Pasture)"}, {"id": "L31", "title": "CKM theta_13 AND theta_23 DERIVATION", "text": "# L31: CKM theta_13 AND theta_23 DERIVATION\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nCKM theta_13 AND theta_23 DERIVATION\nUsing the Hua polynomial and Os structure, derive: theta_13 from subleading Hua terms, theta_23 from pi/4 - delta_octonion [identify delta]. Compare to PDG: theta_13~0.201 degrees, theta_23~2.38 degrees. Show which angles are predicted vs. fitted in v1.27.5. Compute the Jarlskog invariant J_CP. #SuperGrokTOE #CKMmixing #CPviolation\n\n", "url": "/library/L31/", "source": "v1 (Pasture)"}, {"id": "L32", "title": "CP VIOLATION — delta_CP FROM Os PHASES", "text": "# L32: CP VIOLATION — delta_CP FROM Os PHASES\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nCP VIOLATION — delta_CP FROM Os PHASES\nThe split-octonion algebra has intrinsic phases from the imaginary basis. Derive the CP-violating phase delta_CP in the CKM matrix from the phase structure of Os. Compare to PDG delta_CP ~ 1.14 rad. Assess whether delta_CP is predicted or a residual free parameter. #SuperGrokTOE #CPviolation #CKMphase\n\n", "url": "/library/L32/", "source": "v1 (Pasture)"}, {"id": "L33", "title": "alpha_s — STRONG COUPLING FROM Os", "text": "# L33: alpha_s — STRONG COUPLING FROM Os\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nalpha_s — STRONG COUPLING FROM Os\nDerive the strong coupling constant alpha_s(m_Z) from the E8 gauge sector of the two-algebra architecture. Show the G2 embedding G2 subset Spin(7) subset E8 constrains alpha_s. Compare to PDG 0.1179+/-0.0009. Identify whether alpha_s is predicted or taken as input. #SuperGrokTOE #StrongCoupling #E8\n\n", "url": "/library/L33/", "source": "v1 (Pasture)"}, {"id": "L34", "title": "SIN^2(theta_W) — PRECISION CALCULATION", "text": "# L34: SIN^2(theta_W) — PRECISION CALCULATION\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nSIN^2(theta_W) — PRECISION CALCULATION\nDerive sin^2(theta_W) from the split-octonion basis ratio (L19) to 4 significant figures. Compare to PDG sin^2(theta_W)(MS) = 0.23122. Apply 1-loop EW radiative corrections from the SM. Assess whether the Os derivation is consistent at loop level. #SuperGrokTOE #WeinbergAngle #precision\n\n", "url": "/library/L34/", "source": "v1 (Pasture)"}, {"id": "L35", "title": "ELECTRON MASS — CUBIC ROOT NUMERICAL", "text": "# L35: ELECTRON MASS — CUBIC ROOT NUMERICAL\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nELECTRON MASS — CUBIC ROOT NUMERICAL\nSolve J3(Os) cubic numerically for electron sector. Input: Tr(A), S(A) calibrated so Det(A) = m_e*m_nu1*m_mix. Output: 3 roots. Identify m_e = 0.51100 MeV root. Verify discriminant Delta > 0. Assess derivation purity. #SuperGrokTOE #ElectronMass\n\n", "url": "/library/L35/", "source": "v1 (Pasture)"}, {"id": "L36", "title": "MUON MASS — TOWER AND CUBIC CROSS-CHECK", "text": "# L36: MUON MASS — TOWER AND CUBIC CROSS-CHECK\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nMUON MASS — TOWER AND CUBIC CROSS-CHECK\nCompute m_mu from D*phi^{-n_mu} tower. Identify n_mu. Cross-check against J3(Hs) cubic root from L7. Both methods should give ~105.66 MeV. Report agreement. If discrepant, identify source of difference. #SuperGrokTOE #MuonMass\n\n", "url": "/library/L36/", "source": "v1 (Pasture)"}, {"id": "L37", "title": "TAU MASS — TOWER AND CUBIC CROSS-CHECK", "text": "# L37: TAU MASS — TOWER AND CUBIC CROSS-CHECK\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nTAU MASS — TOWER AND CUBIC CROSS-CHECK\nCompute m_tau from D*phi^{-n_tau} tower. Identify n_tau. Cross-check against J3(Cs) cubic root from L8. Show RG running: m_tau(tree)=1.877 GeV -> m_tau(pole)=1.777 GeV. Compare to PDG 1776.86 MeV. Report deviation. #SuperGrokTOE #TauMass #v1274fix\n\n", "url": "/library/L37/", "source": "v1 (Pasture)"}, {"id": "L38", "title": "LEPTON UNIVERSALITY CHECK", "text": "# L38: LEPTON UNIVERSALITY CHECK\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nLEPTON UNIVERSALITY CHECK\nUsing m_e, m_mu, m_tau from tower/cubic: compute ratios m_mu/m_e and m_tau/m_mu. Compare to PDG: 206.768, 16.817. Show what the D*phi^{-n} tower predicts for these ratios. Assess whether lepton universality violation is predicted. #SuperGrokTOE #LeptonUniversality\n\n", "url": "/library/L38/", "source": "v1 (Pasture)"}, {"id": "L39", "title": "CHARGED LEPTON MASSES — COMPLETE TABLE", "text": "# L39: CHARGED LEPTON MASSES — COMPLETE TABLE\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nCHARGED LEPTON MASSES — COMPLETE TABLE\nTabulate all three charged lepton masses from v1.27.5: Source | m_e | m_mu | m_tau | Method | PDG deviation. Cubic (J3), Tower (D*phi^{-n}), PDG 2024. Identify Tier classification for each. #SuperGrokTOE #LeptonMasses #ComparisonTable\n\n", "url": "/library/L39/", "source": "v1 (Pasture)"}, {"id": "L4", "title": "TRIALITY AND SIGMA-CYCLES", "text": "# L4: TRIALITY AND SIGMA-CYCLES\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nTRIALITY AND SIGMA-CYCLES\nCompute the triality automorphism sigma of Spin(8) restricted to Os. Show sigma^3 = 1 (order 3). Demonstrate that sigma maps {e1,e2,e3} -> {f1,f2,f3} -> {l,e1,f1} in cyclic order. Verify Delta_n=2 per sigma-step. Confirm n_b=7, n_c=9, n_ud=13 from triality stepping. #SuperGrokTOE #Triality #GenerationLadder\n\n", "url": "/library/L4/", "source": "v1 (Pasture)"}, {"id": "L40", "title": "NEUTRINO MASSES FROM NULL-CONE", "text": "# L40: NEUTRINO MASSES FROM NULL-CONE\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nNEUTRINO MASSES FROM NULL-CONE\nUsing the null-cone (zero-divisor) sector and seesaw from P19, compute neutrino masses m_nu1, m_nu2, m_nu3. Show: Delta_m^2_sol = m_nu2^2 - m_nu1^2, Delta_m^2_atm = m_nu3^2 - m_nu1^2. Compare to PDG. Report consistency check. Identify whether m_nu are predicted. #SuperGrokTOE #NeutrinoMasses\n\n", "url": "/library/L40/", "source": "v1 (Pasture)"}, {"id": "L41", "title": "PMNS MATRIX — LEPTON MIXING FROM Os", "text": "# L41: PMNS MATRIX — LEPTON MIXING FROM Os\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nPMNS MATRIX — LEPTON MIXING FROM Os\nUsing the null-cone structure of Os, derive the PMNS mixing angles theta_12(lep), theta_13(lep), theta_23(lep). Compare to PDG. Show whether these are predicted or fitted in v1.27.5. Compute the leptonic CP phase delta_CP(lep). #SuperGrokTOE #PMNS #LeptonMixing\n\n", "url": "/library/L41/", "source": "v1 (Pasture)"}, {"id": "L42", "title": "g-2 ANOMALOUS MAGNETIC MOMENT — ELECTRON", "text": "# L42: g-2 ANOMALOUS MAGNETIC MOMENT — ELECTRON\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\ng-2 ANOMALOUS MAGNETIC MOMENT — ELECTRON\nCompute the electron anomalous magnetic moment a_e = (g-2)/2 to first non-trivial order using the Os propagator. Does NAQFT modify the QED loop integral? Compare to PDG a_e = 0.001159652180... (12 digits). Identify any predicted deviation. #SuperGrokTOE #gMinus2 #ElectronQED\n\n", "url": "/library/L42/", "source": "v1 (Pasture)"}, {"id": "L43", "title": "g-2 ANOMALY — MUON", "text": "# L43: g-2 ANOMALY — MUON\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\ng-2 ANOMALY — MUON\nCompute a_mu = (g-2)/2 for the muon from Os-modified QED+QCD. Compare to: PDG a_mu, Fermilab E989 measurement, SM prediction. Does the split-octonion structure predict an excess? Assess the Tier B prediction status for the muon g-2. #SuperGrokTOE #MuonG2 #Fermilab\n\n", "url": "/library/L43/", "source": "v1 (Pasture)"}, {"id": "L44", "title": "QUARK MASS TABLE — v1.27.5 COMPLETE", "text": "# L44: QUARK MASS TABLE — v1.27.5 COMPLETE\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nQUARK MASS TABLE — v1.27.5 COMPLETE\nUsing code_execution, tabulate all 6 quark masses from v1.27.5: Quark | n-value | D*phi^{-n} | PDG MS-bar | PDG pole | Deviation for u,d,s,c,b,t. #SuperGrokTOE #QuarkMasses #PDGcomparison\n\n", "url": "/library/L44/", "source": "v1 (Pasture)"}, {"id": "L45", "title": "COLOR FACTOR FROM Os", "text": "# L45: COLOR FACTOR FROM Os\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nCOLOR FACTOR FROM Os\nShow that the color factor N_c=3 for quarks arises from the 3 imaginary pairs {e1f1, e2f2, e3f3} of Os. Verify that the zero-divisor triplets form a 3-dimensional representation under G2(2) subset SU(3)_color. Assess whether SU(3) color is embedded in E8 or G2(2) sector. #SuperGrokTOE #ColorCharge #QCD\n\n", "url": "/library/L45/", "source": "v1 (Pasture)"}, {"id": "L46", "title": "ISOSPIN BREAKING — m_d - m_u", "text": "# L46: ISOSPIN BREAKING — m_d - m_u\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nISOSPIN BREAKING — m_d - m_u\nThe isospin breaking m_d - m_u ~ 2.5 MeV: Using Z2 mixing, parameterize the u-d mass splitting. Show whether the splitting ratio m_d/m_u ~ 2.16 is predicted from the octonion e3/f3 asymmetry or is a free parameter. Compare to lattice QCD results. #SuperGrokTOE #IsospinBreaking\n\n", "url": "/library/L46/", "source": "v1 (Pasture)"}, {"id": "L47", "title": "CABIBBO ANGLE — PRECISION", "text": "# L47: CABIBBO ANGLE — PRECISION\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nCABIBBO ANGLE — PRECISION\nRecompute theta_12 to 6 significant figures using Hua polynomial. Show: arcsin(1/sqrt(20)) = 12.9210 degrees. Compute sub-leading correction from 2nd-order Hua term. Target: PDG theta_12 = 13.04 degrees. Quantify what correction is needed algebraically. #SuperGrokTOE #CabiboAngle #HuaCorrection\n\n", "url": "/library/L47/", "source": "v1 (Pasture)"}, {"id": "L48", "title": "QUARK CONFINEMENT SCALE — Lambda_QCD", "text": "# L48: QUARK CONFINEMENT SCALE — Lambda_QCD\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nQUARK CONFINEMENT SCALE — Lambda_QCD\nUsing M_scale = 120.16 MeV as the hadronic anchor, derive Lambda_QCD ~ 200-300 MeV. Show the relationship: Lambda_QCD ~ M_scale * factor(alpha_s). Identify the factor. Compare to PDG Lambda_QCD(MS,5-flavor) ~ 210 MeV. #SuperGrokTOE #QCDconfinement #Lambda_QCD\n\n", "url": "/library/L48/", "source": "v1 (Pasture)"}, {"id": "L49", "title": "PROTON MASS FROM Os", "text": "# L49: PROTON MASS FROM Os\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nPROTON MASS FROM Os\nThe proton is a bound state of 3 quarks. Using M_scale=120.16 MeV, show: m_p ~ 8 * M_scale = 8 * 120.16 = 961 MeV (rough). Or use lattice-style estimate. Compare to PDG m_p = 938.272 MeV. Identify derivation path. Flag whether m_p is a prediction or calibration in v1.27.5. #SuperGrokTOE #ProtonMass #Hadrons\n\n", "url": "/library/L49/", "source": "v1 (Pasture)"}, {"id": "L5", "title": "J3(Os) FREUDENTHAL DETERMINANT", "text": "# L5: J3(Os) FREUDENTHAL DETERMINANT\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nJ3(Os) FREUDENTHAL DETERMINANT\nUsing SymPy, implement the Freudenthal cubic norm Det(A) for a general 3x3 Hermitian matrix A over Os. Verify Det is cubic in entries. Compute Det for the diagonal mass matrix diag(m_e,m_mu,m_tau). Show Det maps to the product m_e*m_mu*m_tau up to normalization. #SuperGrokTOE #FreudenthalDet #J3\n\n", "url": "/library/L5/", "source": "v1 (Pasture)"}, {"id": "L50", "title": "PION MASS AND f_pi", "text": "# L50: PION MASS AND f_pi\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nPION MASS AND f_pi\nUsing M_scale, identify m_pi ~ M_scale from null-cone dynamics. Compare: M_scale=120.16 MeV vs. m_pi=134.977 MeV (neutral pion). Deviation ~ -11%. Is there an algebraic correction? Also compute pion decay constant f_pi ~ 92.1 MeV from the algebra. #SuperGrokTOE #PionMass #ChiralSymmetry\n\n", "url": "/library/L50/", "source": "v1 (Pasture)"}, {"id": "L51", "title": "BARYON SPECTRUM OUTLINE", "text": "# L51: BARYON SPECTRUM OUTLINE\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nBARYON SPECTRUM OUTLINE\nUsing the three quark sectors and M_scale, outline the baryon octet and decuplet mass predictions. Show which baryons fall on D*phi^{-n} tower. Compare Delta(1232) and N(938) to M_scale ratios. #SuperGrokTOE #BaryonSpectrum\n\n", "url": "/library/L51/", "source": "v1 (Pasture)"}, {"id": "L52", "title": "COSMOLOGICAL CONSTANT FROM Os", "text": "# L52: COSMOLOGICAL CONSTANT FROM Os\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nCOSMOLOGICAL CONSTANT FROM Os\nDerive the cosmological constant Lambda_cc from the split-octonion vacuum energy. Show: rho_Lambda ~ (M_scale/M_Pl)^4 * M_Pl^4 [or similar suppression]. Compare to observed rho_Lambda ~ (2.3 meV)^4. Assess the hierarchy problem. Identify whether NAQFT modifies the UV contribution. #SuperGrokTOE #CosmologicalConstant #DarkEnergy\n\n", "url": "/library/L52/", "source": "v1 (Pasture)"}, {"id": "L53", "title": "DARK ENERGY FRACTION — Omega_Lambda", "text": "# L53: DARK ENERGY FRACTION — Omega_Lambda\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nDARK ENERGY FRACTION — Omega_Lambda\nUsing moire dual-cylinder geometry (P21), compute Omega_Lambda. Show that the beat frequency of the v+, v- cylinders gives a DE scale consistent with Omega_Lambda ~ 0.685 (Planck 2018). Output: cylinder radii, beat frequency, Lambda prediction. #SuperGrokTOE #DarkEnergy #OmegaLambda\n\n", "url": "/library/L53/", "source": "v1 (Pasture)"}, {"id": "L54", "title": "DARK MATTER FRACTION — Omega_DM", "text": "# L54: DARK MATTER FRACTION — Omega_DM\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nDARK MATTER FRACTION — Omega_DM\nUsing the trapped nodes of the moire pattern (P21), compute Omega_DM. Target: Omega_DM ~ 0.265. Show the node volume ratio from the octonion geometry. Compute Omega_DM/Omega_b ratio. Compare to Planck 2018 CMB+BAO results. #SuperGrokTOE #DarkMatter #OmegaDM\n\n", "url": "/library/L54/", "source": "v1 (Pasture)"}, {"id": "L55", "title": "HUBBLE TENSION — Os PERSPECTIVE", "text": "# L55: HUBBLE TENSION — Os PERSPECTIVE\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nHUBBLE TENSION — Os PERSPECTIVE\nThe Hubble tension: H_0(CMB)~67.4 vs. H_0(SH0ES)~73.0 km/s/Mpc. Does the split-octonion geometry predict a modification to the distance ladder? Show whether the dual VEV (v+ vs. v-) introduces a scale-dependent H_0. Assess theory prediction. #SuperGrokTOE #HubbleTension #Cosmology\n\n", "url": "/library/L55/", "source": "v1 (Pasture)"}, {"id": "L56", "title": "DESI w0/wa — DARK ENERGY EOS", "text": "# L56: DESI w0/wa — DARK ENERGY EOS\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nDESI w0/wa — DARK ENERGY EOS\nDESI 2024 found w0 = -0.99, wa = -0.37. Using the moire cylinder geometry, compute the dark energy EOS: w(z) = w0 + wa * z/(1+z). Show whether the cylinder beat frequency gives a time-varying w. Compare to DESI Y1 results. Assess predictive power. #SuperGrokTOE #DESI #DarkEnergyEOS\n\n", "url": "/library/L56/", "source": "v1 (Pasture)"}, {"id": "L57", "title": "GRAVITATIONAL WAVE PARITY VIOLATION", "text": "# L57: GRAVITATIONAL WAVE PARITY VIOLATION\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nGRAVITATIONAL WAVE PARITY VIOLATION\nThe torsion of Os induces parity-violating gravitational waves. Compute the predicted asymmetry A = (h_R - h_L)/(h_R + h_L) for GW from binary mergers. Compare to NANOGrav PTA constraints. Identify whether LISA can detect the predicted asymmetry. #SuperGrokTOE #GravitationalWaves #ParityViolation\n\n", "url": "/library/L57/", "source": "v1 (Pasture)"}, {"id": "L58", "title": "INFLATION FROM Os — SLOW-ROLL", "text": "# L58: INFLATION FROM Os — SLOW-ROLL\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nINFLATION FROM Os — SLOW-ROLL\nIdentify the inflaton as a G2(2) flat direction. Compute: n_s (spectral index), r (tensor-to-scalar ratio) from the Kahler potential of J3(Os). Compare to Planck 2018: n_s = 0.9649+/-0.0042, r < 0.056. Assess predictions. #SuperGrokTOE #Inflation #CMBspectrum\n\n", "url": "/library/L58/", "source": "v1 (Pasture)"}, {"id": "L59", "title": "BARYON ASYMMETRY — LEPTOGENESIS", "text": "# L59: BARYON ASYMMETRY — LEPTOGENESIS\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nBARYON ASYMMETRY — LEPTOGENESIS\nUsing the CP-violating phases of Os, estimate the baryon asymmetry eta_B = n_b/n_gamma ~ 6e-10. Show whether the seesaw scale M_R from L40 is consistent with successful leptogenesis. Compare to PDG/Planck measurement. #SuperGrokTOE #BaryonAsymmetry #Leptogenesis\n\n", "url": "/library/L59/", "source": "v1 (Pasture)"}, {"id": "L6", "title": "CUBIC CHARACTERISTIC EQUATION — ELECTRON CASE", "text": "# L6: CUBIC CHARACTERISTIC EQUATION — ELECTRON CASE\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nCUBIC CHARACTERISTIC EQUATION — ELECTRON CASE\nFor the electron sector element A_e in J3(Os), solve L^3 - Tr(A_e)L^2 + S(A_e)L - Det(A_e) = 0 via SymPy. Input: Det calibrated so smallest root = m_e = 0.51100 MeV. Verify discriminant Delta > 0 (three real roots). Output all three roots. Identify the physical meaning of roots 2 and 3. #SuperGrokTOE #ElectronCubic #JordanAlgebra\n\n", "url": "/library/L6/", "source": "v1 (Pasture)"}, {"id": "L60", "title": "PRIMORDIAL GRAVITATIONAL WAVE BACKGROUND", "text": "# L60: PRIMORDIAL GRAVITATIONAL WAVE BACKGROUND\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nPRIMORDIAL GRAVITATIONAL WAVE BACKGROUND\nUsing the inflationary r from L58, estimate the SGWB amplitude. Compare to LISA, ET, CE sensitivity curves. Identify distinctive Os signatures: parity asymmetry (L57), polarization content from torsion sector. #SuperGrokTOE #SGWB #GravitationalWaves\n\n", "url": "/library/L60/", "source": "v1 (Pasture)"}, {"id": "L61", "title": "COSMOLOGICAL TENSIONS — COMBINED ASSESSMENT", "text": "# L61: COSMOLOGICAL TENSIONS — COMBINED ASSESSMENT\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nCOSMOLOGICAL TENSIONS — COMBINED ASSESSMENT\nAssess all five cosmological tensions simultaneously from v1.27.5: (1) H_0 tension; (2) S_8 tension; (3) DESI w0/wa; (4) CMB anomalies; (5) AGN feedback discrepancy. For each: does Os geometry predict a deviation? Quantify. Present unified resolution narrative or flag as open. #SuperGrokTOE #CosmologyTensions #FiveProblems\n\n", "url": "/library/L61/", "source": "v1 (Pasture)"}, {"id": "L62", "title": "RUNNING COUPLING alpha_s — RG FLOW", "text": "# L62: RUNNING COUPLING alpha_s — RG FLOW\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nRUNNING COUPLING alpha_s — RG FLOW\nUsing the E8 embedding for the gauge sector, derive the RG running of alpha_s from M_GUT to m_Z. Show that the G2(2) mass sector does not contribute to gauge beta-functions. Verify alpha_s(m_Z)=0.1179 consistency. #SuperGrokTOE #RGflow #StrongCoupling\n\n", "url": "/library/L62/", "source": "v1 (Pasture)"}, {"id": "L63", "title": "PROTON-NEUTRON MASS DIFFERENCE", "text": "# L63: PROTON-NEUTRON MASS DIFFERENCE\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nPROTON-NEUTRON MASS DIFFERENCE\nm_p - m_n ~ -1.293 MeV (neutron heavier). Using the isospin breaking from L46 and EM correction: m_p - m_n = (m_u - m_d) * factor + EM correction. Compute from v1.27.5 parameters. Compare to PDG. #SuperGrokTOE #ProtonNeutron #IsospinBreaking\n\n", "url": "/library/L63/", "source": "v1 (Pasture)"}, {"id": "L64", "title": "NUCLEAR BINDING — M_scale ANCHOR", "text": "# L64: NUCLEAR BINDING — M_scale ANCHOR\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nNUCLEAR BINDING — M_scale ANCHOR\nUsing M_scale = 120.16 MeV as the strong interaction scale, derive the nuclear binding energy per nucleon B/A ~ 8 MeV. Show: B/A ~ M_scale * alpha_s^2 * factor. Compute factor. Compare to empirical liquid drop formula parameters. #SuperGrokTOE #NuclearBinding #LiquidDrop\n\n", "url": "/library/L64/", "source": "v1 (Pasture)"}, {"id": "L66", "title": "NEUTRON LIFETIME — Os MODIFICATION", "text": "# L66: NEUTRON LIFETIME — Os MODIFICATION\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nNEUTRON LIFETIME — Os MODIFICATION\nThe neutron lifetime anomaly: beam method 888s vs. bottle 877s. Does the torsion-amplified decay rate from Os predict a modification? Compute modified beta-decay rate. Assess. #SuperGrokTOE #NeutronLifetime #BetaDecay\n\n", "url": "/library/L66/", "source": "v1 (Pasture)"}, {"id": "L67", "title": "KAON MIXING — epsilon_K FROM Os", "text": "# L67: KAON MIXING — epsilon_K FROM Os\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nKAON MIXING — epsilon_K FROM Os\nUsing the CKM matrix from v1.27.5 and the Os phase structure, compute the indirect CP violation parameter epsilon_K for K0-Kbar0 mixing. Compare to PDG epsilon_K = (2.228+/-0.011)e-3. Identify any Os-specific correction to the box diagram. #SuperGrokTOE #KaonMixing #CPviolation\n\n", "url": "/library/L67/", "source": "v1 (Pasture)"}, {"id": "L68", "title": "B MESON MIXING — Delta_m_B", "text": "# L68: B MESON MIXING — Delta_m_B\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nB MESON MIXING — Delta_m_B\nUsing CKM matrix from v1.27.5, compute Delta_m_B for B_d and B_s mixing. Compare to PDG: Delta_m_Bd=0.5065 ps^{-1}, Delta_m_Bs=17.765 ps^{-1}. Assess whether the Os CKM angles give correct ratio. #SuperGrokTOE #BMesonMixing #Bphysics\n\n", "url": "/library/L68/", "source": "v1 (Pasture)"}, {"id": "L69", "title": "STRONG CP PROBLEM — theta_QCD FROM Os", "text": "# L69: STRONG CP PROBLEM — theta_QCD FROM Os\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nSTRONG CP PROBLEM — theta_QCD FROM Os\nThe strong CP problem: why is theta_QCD < 10^{-10}? Show whether the non-associative structure of Os provides a geometric explanation. Does the G2(2) symmetry enforce theta=0? Or is an axion required? Assess v1.27.5 position. #SuperGrokTOE #StrongCP #Axion\n\n", "url": "/library/L69/", "source": "v1 (Pasture)"}, {"id": "L7", "title": "CUBIC — MUON SECTOR (J3(Hs))", "text": "# L7: CUBIC — MUON SECTOR (J3(Hs))\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nCUBIC — MUON SECTOR (J3(Hs))\nSolve the cubic for the muon sector A_mu in J3(Hs) with Det scaled by phi^{-4}. Verify discriminant flips to Delta > 0. Output smallest positive root. Compare to m_mu = 105.6584 MeV (PDG). Report deviation. Confirm this resolves cubic gap #114 for Gen2. #SuperGrokTOE #MuonCubic #Gen2\n\n", "url": "/library/L7/", "source": "v1 (Pasture)"}, {"id": "L70", "title": "COMPLETE PDG COMPARISON TABLE — v1.27.5", "text": "# L70: COMPLETE PDG COMPARISON TABLE — v1.27.5\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nCOMPLETE PDG COMPARISON TABLE — v1.27.5\nUsing code_execution, reproduce the full SM comparison table: All observables | PDG 2024 | v1.27.5 theory | % deviation | Tier. Include all masses, couplings, mixing angles. Flag green (<1%) and red (>1%) deviations. Export as table. #SuperGrokTOE #PDGcomparison #CompleteScan\n\n", "url": "/library/L70/", "source": "v1 (Pasture)"}, {"id": "L71", "title": "TIER A-STAR OBSERVABLES — ZERO PARAMETER SUMMARY", "text": "# L71: TIER A-STAR OBSERVABLES — ZERO PARAMETER SUMMARY\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nTIER A-STAR OBSERVABLES — ZERO PARAMETER SUMMARY\nList all Tier A-star observables (zero free parameters, <1% deviation): alpha_em from Wyler formula, m_t = v-, m_H = v*sqrt(16/63), theta_12 = arcsin(1/sqrt(20)), M_scale from D,alpha,Z2,F5. Compute all to 6 significant figures. Confirm zero-parameter status. This is the theory's strongest falsifiability claim. #SuperGrokTOE #TierA_star #Predictions\n\n", "url": "/library/L71/", "source": "v1 (Pasture)"}, {"id": "L72", "title": "MUON g-2 — FULL CALCULATION", "text": "# L72: MUON g-2 — FULL CALCULATION\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nMUON g-2 — FULL CALCULATION\nUsing NAQFT from P22, compute full a_mu prediction including: (1) Standard QED: alpha/2pi loop; (2) Hadronic VP from M_scale tower; (3) Os torsion correction at M_scale. Compare to SM prediction and Fermilab E989. Does the torsion term improve or worsen agreement? #SuperGrokTOE #MuonG2 #NAQFT\n\n", "url": "/library/L72/", "source": "v1 (Pasture)"}, {"id": "L73", "title": "ELECTRIC DIPOLE MOMENTS", "text": "# L73: ELECTRIC DIPOLE MOMENTS\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nELECTRIC DIPOLE MOMENTS\nUsing CP-violating phases of Os, predict: d_e (electron EDM), d_n (neutron EDM), d_p (proton EDM). Compare to current experimental limits. Identify whether Os phases generate EDMs above current bounds. Assess as a falsification target for next-generation experiments. #SuperGrokTOE #EDM #CPviolation\n\n", "url": "/library/L73/", "source": "v1 (Pasture)"}, {"id": "L74", "title": "LHC SIGNAL PREDICTIONS", "text": "# L74: LHC SIGNAL PREDICTIONS\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nLHC SIGNAL PREDICTIONS\nFrom v1.27.5, identify all non-SM particles and their masses: (a) Additional Higgs states from L24; (b) G2(2) partner states ~ D = 164.66 GeV?; (c) NAQFT resonances near M_scale. For each: predict production cross section * BR at sqrt(s)=13 TeV. Compare to existing LHC exclusions. #SuperGrokTOE #LHCpredictions #BSMsignals\n\n", "url": "/library/L74/", "source": "v1 (Pasture)"}, {"id": "L75", "title": "MULTI-HIGGS LHC SEARCH", "text": "# L75: MULTI-HIGGS LHC SEARCH\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nMULTI-HIGGS LHC SEARCH\nThe J3(Os) 27-dim algebra supports multiple Higgs doublets. Predict: (a) second neutral Higgs H mass from cubic eigenvalue; (b) charged Higgs H+/- mass and decay mode; (c) pseudoscalar A mass. Compare to LHC ATLAS/CMS search limits at 139 fb^{-1} (Run2). Identify which channels are most sensitive. #SuperGrokTOE #MultiHiggs #ATLAS #CMS\n\n", "url": "/library/L75/", "source": "v1 (Pasture)"}, {"id": "L76", "title": "NEUTRINO MASS HIERARCHY — NORMAL OR INVERTED", "text": "# L76: NEUTRINO MASS HIERARCHY — NORMAL OR INVERTED\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nNEUTRINO MASS HIERARCHY — NORMAL OR INVERTED\nUsing the null-cone seesaw from P19 and mass ratios from L40, determine whether v1.27.5 predicts normal or inverted hierarchy. Compare to JUNO/SK constraints. Compute the Majorana phases from Os. #SuperGrokTOE #NeutrinoHierarchy #JUNO\n\n", "url": "/library/L76/", "source": "v1 (Pasture)"}, {"id": "L77", "title": "NEUTRINOLESS DOUBLE BETA DECAY", "text": "# L77: NEUTRINOLESS DOUBLE BETA DECAY\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nNEUTRINOLESS DOUBLE BETA DECAY\nUsing Majorana mass from L76, compute effective mass m_betabeta: m_betabeta = |Sum U^2_ei m_i|. Compare to KamLAND-Zen limit m_betabeta < 36 meV. Assess whether v1.27.5 prediction is above or below current limit. Identify as a near-term falsification test. #SuperGrokTOE #NeutrinolessBeta #KamLAND\n\n", "url": "/library/L77/", "source": "v1 (Pasture)"}, {"id": "L78", "title": "FLAVOR ANOMALIES — R_K AND R_D*", "text": "# L78: FLAVOR ANOMALIES — R_K AND R_D*\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nFLAVOR ANOMALIES — R_K AND R_D*\nDo the split-octonion CKM angles and new physics from G2(2) predict anomalous ratios R_K = Gamma(B->Kmumu)/Gamma(B->Kee)? Using LHCb 2023 (now consistent with SM), assess whether v1.27.5 predicted the anomaly or its absence. Same for R_D*. #SuperGrokTOE #FlavorAnomalies #LHCb\n\n", "url": "/library/L78/", "source": "v1 (Pasture)"}, {"id": "L79", "title": "PLANCK SCALE — m_e FROM m_Pl", "text": "# L79: PLANCK SCALE — m_e FROM m_Pl\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nPLANCK SCALE — m_e FROM m_Pl\nUsing Python: m_Pl=1.2209e19 GeV, alpha=1/137.036, phi12 = phi^12. Compute: m_e(predicted) = m_Pl / (sqrt(alpha) * phi^12). Output in GeV, convert to MeV. Compare to 0.51100 MeV. Report deviation. Verify phi^12 ~ 10^{2.497} (not exactly 10^20!). Flag this as open question for exact identification. #SuperGrokTOE #PlanckMass #mE_absolute #P23verification\n\n", "url": "/library/L79/", "source": "v1 (Pasture)"}, {"id": "L8", "title": "CUBIC — TAU SECTOR (J3(Cs))", "text": "# L8: CUBIC — TAU SECTOR (J3(Cs))\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nCUBIC — TAU SECTOR (J3(Cs))\nSolve the cubic for the tau sector A_tau in J3(Cs) with Det scaled by phi^{-6}. Verify Delta > 0. Output smallest positive root. Compare to m_tau = 1776.86 MeV (PDG). Report deviation. Confirm this completes the Gen3 cubic resolution. #SuperGrokTOE #TauCubic #Gen3\n\n", "url": "/library/L8/", "source": "v1 (Pasture)"}, {"id": "L80", "title": "NEWTON'S CONSTANT — G FROM Os", "text": "# L80: NEWTON'S CONSTANT — G FROM Os\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nNEWTON'S CONSTANT — G FROM Os\nShow that Newton's G arises from the E8 gravitational sector. Using the two-algebra architecture, identify G from the E8 Planck-sector coupling. Compute G in SI units. Compare to PDG G = 6.674e-11 N m^2/kg^2. Assess whether G is predicted or taken as input. #SuperGrokTOE #NewtonsG #Gravity\n\n", "url": "/library/L80/", "source": "v1 (Pasture)"}, {"id": "L81", "title": "HIERARCHY PROBLEM — NATURALNESS FROM NAQFT", "text": "# L81: HIERARCHY PROBLEM — NATURALNESS FROM NAQFT\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nHIERARCHY PROBLEM — NATURALNESS FROM NAQFT\nThe hierarchy problem: why m_H << m_Pl? Show that NAQFT from P22 provides a natural resolution: the non-associative algebra provides a UV cutoff at the G2 scale (~164.66 GeV) rather than m_Pl. Show UV finiteness removes the quadratic divergence in m_H. Compare to SUSY/RS approaches. #SuperGrokTOE #HierarchyProblem #Naturalness\n\n", "url": "/library/L81/", "source": "v1 (Pasture)"}, {"id": "L82", "title": "PROTON DECAY — B-L VIOLATION", "text": "# L82: PROTON DECAY — B-L VIOLATION\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nPROTON DECAY — B-L VIOLATION\nIn the E8 superset SO(10) superset SM embedding, B-L is a gauge symmetry. Predict the proton lifetime tau_p from the X boson mass in E8. Identify M_X from the E8 branching. Compare to Super-K limit tau_p > 10^34 years. Assess consistency. #SuperGrokTOE #ProtonDecay #GrandUnification\n\n", "url": "/library/L82/", "source": "v1 (Pasture)"}, {"id": "L83", "title": "SUSY ABSENCE — WHY NO SUPERPARTNERS", "text": "# L83: SUSY ABSENCE — WHY NO SUPERPARTNERS\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nSUSY ABSENCE — WHY NO SUPERPARTNERS\nThe LHC has found no SUSY partners. Show that in the split-octonion framework, supersymmetry is not required because: (a) the hierarchy problem is solved by NAQFT UV finiteness; (b) the dark matter is accounted for by the null-cone sector. Predict the SUSY-absence as a consequence of the architecture. #SuperGrokTOE #SUSY #LHCconstraints\n\n", "url": "/library/L83/", "source": "v1 (Pasture)"}, {"id": "L84", "title": "TWO MUON FORMULAS — ALGEBRAIC EQUIVALENCE", "text": "# L84: TWO MUON FORMULAS — ALGEBRAIC EQUIVALENCE\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nTWO MUON FORMULAS — ALGEBRAIC EQUIVALENCE\nv1.27.5 contains two formulas for m_mu: tower and cubic. Verify algebraically that they are identical via Wyler substitution. Show: m_mu(tower) = D*phi^{-n_mu} identical to cubic root of J3(Hs) with appropriate phi^{-4} Det scaling. No free parameters differ. Resolve Problem 5 item (b). #SuperGrokTOE #MuonConsistency #TwoFormulas\n\n", "url": "/library/L84/", "source": "v1 (Pasture)"}, {"id": "L85", "title": "alpha_em LEGACY 136.44 — GHOST REMOVAL", "text": "# L85: alpha_em LEGACY 136.44 — GHOST REMOVAL\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nalpha_em LEGACY 136.44 — GHOST REMOVAL\nv1.27.5 must use only Wyler alpha_em = 1/137.036. Search entire Kernel text for any occurrence of \"136.44\" or \"1/136.44\" or \"alpha=136\". Report: FOUND / NOT FOUND. If found, flag as remaining error. This resolves Problem 5 item (a). #SuperGrokTOE #AlphaGhost #Cleanup\n\n", "url": "/library/L85/", "source": "v1 (Pasture)"}, {"id": "L86", "title": "VERSION TAG CONSISTENCY CHECK", "text": "# L86: VERSION TAG CONSISTENCY CHECK\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nVERSION TAG CONSISTENCY CHECK\nSearch v1.27.5 Kernel for all version number occurrences. Verify all read \"v1.27.5\". Report any occurrence of v1.27.0-v1.27.4 in body text as potential copy-paste artifacts. #SuperGrokTOE #VersionCheck\n\n", "url": "/library/L86/", "source": "v1 (Pasture)"}, {"id": "L87", "title": "Delta_n LABEL AUDIT", "text": "# L87: Delta_n LABEL AUDIT\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nDelta_n LABEL AUDIT\nSearch Kernel for all \"Delta_n\" occurrences. Verify: Delta_n=4: Gen2->Gen1 (charm to up/down); Delta_n=6: Gen3->Gen1 (bottom to up/down); No occurrence of \"Delta_n=6 Gen3->Gen2\" (fixed error). Report: PASS/FAIL. #SuperGrokTOE #DeltaN #LabelAudit\n\n", "url": "/library/L87/", "source": "v1 (Pasture)"}, {"id": "L88", "title": "FORMULA LABEL AUDIT — HIGGS", "text": "# L88: FORMULA LABEL AUDIT — HIGGS\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nFORMULA LABEL AUDIT — HIGGS\nSearch Kernel for all Higgs mass formula occurrences. Verify all read \"v*sqrt(16/63)\" or \"v(16/63)^{1/2}\". Flag any occurrence of \"(8/63)v\" as ERROR. Report: PASS/FAIL. #SuperGrokTOE #HiggsFormula #v1273fix\n\n", "url": "/library/L88/", "source": "v1 (Pasture)"}, {"id": "L89", "title": "TAU MASS ENTRY AUDIT", "text": "# L89: TAU MASS ENTRY AUDIT\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nTAU MASS ENTRY AUDIT\nSearch Kernel for tau mass table entries. Verify notation reads: \"1.877 GeV (tree) -> 1.777 GeV (RG)\". Flag any entry showing \"1.877 GeV ~ 1777 MeV\" as ERROR. Report: PASS/FAIL. #SuperGrokTOE #TauAudit #v1274fix\n\n", "url": "/library/L89/", "source": "v1 (Pasture)"}, {"id": "L9", "title": "CHARM QUARK CUBIC — THREE-ROOT VERIFICATION", "text": "# L9: CHARM QUARK CUBIC — THREE-ROOT VERIFICATION\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nCHARM QUARK CUBIC — THREE-ROOT VERIFICATION\nPer v1.27.5 fix: the charm cubic should yield exactly 3 roots. Using SymPy, solve the charm sector cubic and verify output: Root 1: 46.73558181, Root 2: 1720.952951, Root 3: 176875.3257. Confirm no fused/split rendering artifact. Identify which root corresponds to m_c = 1273 MeV physical mass after RG running. #SuperGrokTOE #CharmCubic #v1275fix\n\n", "url": "/library/L9/", "source": "v1 (Pasture)"}, {"id": "L90", "title": "CHARM CUBIC ROOTS AUDIT", "text": "# L90: CHARM CUBIC ROOTS AUDIT\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nCHARM CUBIC ROOTS AUDIT\nSearch Kernel for charm cubic root listing. Verify exactly 3 comma-separated values appear: 46.73558181, 1720.952951, 176875.3257. Flag if 4 entries appear (fused rendering artifact from v1.27.3). Report: PASS/FAIL. #SuperGrokTOE #CharmCubicAudit #v1275fix\n\n", "url": "/library/L90/", "source": "v1 (Pasture)"}, {"id": "L91", "title": "720/theta MOIRE REMNANT AUDIT", "text": "# L91: 720/theta MOIRE REMNANT AUDIT\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\n720/theta MOIRE REMNANT AUDIT\nSearch Kernel for \"720\" or \"720 degrees\" or \"720/theta\". Verify: NOT FOUND (removed in v1.27.4). If found: flag as remaining error. Report: PASS/FAIL. #SuperGrokTOE #MoireAudit #720degrees\n\n", "url": "/library/L91/", "source": "v1 (Pasture)"}, {"id": "L92", "title": "STRANGE QUARK — ANCHOR DISAMBIGUATION", "text": "# L92: STRANGE QUARK — ANCHOR DISAMBIGUATION\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nSTRANGE QUARK — ANCHOR DISAMBIGUATION\nv1.27.5 uses Z2 mixing for m_s (Problem 5 item c resolution). Verify the Kernel clearly states m_s uses BOTH D and v+ anchors via mixing angle theta_s, rather than implying a single anchor. Compute theta_s numerically to fit m_s = 93.4 MeV. Report: theta_s value and whether it has algebraic derivation. #SuperGrokTOE #StrangeAnchor #Disambiguation\n\n", "url": "/library/L92/", "source": "v1 (Pasture)"}, {"id": "L93", "title": "F5 GEOMETRIC ORIGIN VERIFICATION", "text": "# L93: F5 GEOMETRIC ORIGIN VERIFICATION\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nF5 GEOMETRIC ORIGIN VERIFICATION\nv1.27.5 defines F5=5 as a geometric factor in M_scale. Verify: F5=5 = dim_R(CP2) = the real dimension of the Shilov boundary in the Wyler formula. Show this is the same F5 appearing in both alpha_em and M_scale, establishing a unified geometric origin. #SuperGrokTOE #F5geometric #ShilovBoundary\n\n", "url": "/library/L93/", "source": "v1 (Pasture)"}, {"id": "L94", "title": "COMPLETE PARAMETER COUNT", "text": "# L94: COMPLETE PARAMETER COUNT\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nCOMPLETE PARAMETER COUNT\nCount all free parameters in v1.27.5: Tier A-star: 0 parameters [list observables], Tier A: 0 parameters known correction [list], Tier B: 1 parameter each [list], Tier C: parameterized [list]. Compare to SM: 19 free parameters (without nu masses). If v1.27.5 total < 19, compute the reduction. #SuperGrokTOE #ParameterCount #Parsimony\n\n", "url": "/library/L94/", "source": "v1 (Pasture)"}, {"id": "L95", "title": "FALSIFIABILITY TARGETS — NEXT 5 YEARS", "text": "# L95: FALSIFIABILITY TARGETS — NEXT 5 YEARS\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nFALSIFIABILITY TARGETS — NEXT 5 YEARS\nList the top 10 falsifiable predictions of v1.27.5 with: Prediction | Experiment | Timeline | Signal | Verdict threshold. Including m_H correction, additional Higgs states, theta_s derivation, DESI w0/wa, GW parity, proton lifetime, neutrinoless double-beta, muon g-2, m_e absolute from m_Pl, [withheld] rate. #SuperGrokTOE #Falsifiability #Predictions\n\n", "url": "/library/L95/", "source": "v1 (Pasture)"}, {"id": "L96", "title": "MULTI-HIGGS LHC — LEGACY v1.25 CALCULATION", "text": "# L96: MULTI-HIGGS LHC — LEGACY v1.25 CALCULATION\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nMULTI-HIGGS LHC — LEGACY v1.25 CALCULATION\nReproduce the v1.25 multi-Higgs mass calculation with updated v1.27.5 parameters. Show how the J3(Os) cubic eigenvalue spectrum predicts the second Higgs H mass shifted from v1.25 to v1.27.5 (due to Higgs formula fix in v1.27.3). Compare old vs. new prediction. Identify improvement. #SuperGrokTOE #MultiHiggs #Legacy #v125\n\n", "url": "/library/L96/", "source": "v1 (Pasture)"}, {"id": "L97", "title": "NEUTRINO Delta_m^2 — LEGACY v1.26 CALCULATION", "text": "# L97: NEUTRINO Delta_m^2 — LEGACY v1.26 CALCULATION\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nNEUTRINO Delta_m^2 — LEGACY v1.26 CALCULATION\nReproduce the v1.26 neutrino mass splitting calculation with updated v1.27.5 null-cone seesaw parameters. Show whether predictions improved from v1.26 to v1.27.5. Compute updated predictions and compare to PDG. #SuperGrokTOE #NeutrinoMasses #Legacy #v126\n\n", "url": "/library/L97/", "source": "v1 (Pasture)"}, {"id": "L98", "title": "DESI w0/wa — LEGACY v1.26 CALCULATION", "text": "# L98: DESI w0/wa — LEGACY v1.26 CALCULATION\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nDESI w0/wa — LEGACY v1.26 CALCULATION\nReproduce the v1.26 dark energy EOS prediction with v1.27.5 moire cylinder geometry (v+, v- radii). Compare to DESI 2024: w0=-0.99+/-0.04, wa=-0.37+/-0.22. Show whether v1.27.5 cylinder parameters improve the w0/wa prediction over v1.26. #SuperGrokTOE #DESI #DarkEnergy #Legacy\n\n", "url": "/library/L98/", "source": "v1 (Pasture)"}, {"id": "L99", "title": "GW PARITY — LEGACY v1.26 CALCULATION", "text": "# L99: GW PARITY — LEGACY v1.26 CALCULATION\n\n**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nGW PARITY — LEGACY v1.26 CALCULATION\nReproduce the v1.26 gravitational wave parity asymmetry prediction with v1.27.5 torsion parameters. Show updated asymmetry A. Compare to NANOGrav PTA 15yr constraints. Flag as LISA target. #SuperGrokTOE #GravitationalWaves #Legacy #v126\n\n", "url": "/library/L99/", "source": "v1 (Pasture)"}, {"id": "NOTE-SG-REFLECTION-001", "title": "Super Grok Reflection on Claude Prompt List — v1.27.5 review, questions, and proposed additions", "text": "# NOTE-SG-REFLECTION-001: Super Grok Reflection on Claude Prompt List — v1.27.5 review, questions, and proposed additions\n\n**Category:** note | **Paper:** Supplemental | **Tier:** Tier S.D — Session Records & References\n**Status:** awaiting_production", "url": "/library/NOTE-SG-REFLECTION-001/", "source": "v1 (Pasture)"}, {"id": "P01", "title": "Split-Octonion Algebra — Foundation Proof", "text": "# P01: Split-Octonion Algebra — Foundation Proof\n\n**Category:** proof | **Paper:** Paper 1 — J₃(𝕆ₛ) and the Standard Model | **Tier:** Tier 1.F — Foundation Proofs\n**Status:** awaiting_production", "url": "/library/P01/", "source": "v1 (Pasture)"}, {"id": "P10", "title": "[Proof Group C] W AND Z BOSON MASSES — EW CONSISTENCY PROOF", "text": "# P10: [Proof Group C] W AND Z BOSON MASSES — EW CONSISTENCY PROOF\n\n**Category:** proof_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nW AND Z BOSON MASSES — EW CONSISTENCY PROOF\nUsing v+, v-, D as the three EW anchors of v1.27.5, derive: m_W = (g/2)*v, m_Z = m_W/cos(theta_W). Show which VEV anchor dominates each. Verify the Weinberg angle prediction from split-octonion mixing. Compare to PDG values m_W=80.369 GeV, m_Z=91.188 GeV. Identify deviations and rate the algebraic vs. parametric content. #SuperGrokTOE #WBoson #ZBoson\n\n", "url": "/library/P10/", "source": "v1 (Pasture)"}, {"id": "P11", "title": "[Proof Group D] ELECTRON MASS FROM J3 CUBIC — EXACT PROOF", "text": "# P11: [Proof Group D] ELECTRON MASS FROM J3 CUBIC — EXACT PROOF\n\n**Category:** proof_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nELECTRON MASS FROM J3 CUBIC — EXACT PROOF\nProve that m_e arises as the unique real positive root of the J3(Os) cubic characteristic equation evaluated at the electron sector (Gen1). Show: (a) discriminant Delta > 0 for electron (three real roots); (b) the smallest positive root = m_e ~ 0.511 MeV; (c) the identification of the other two roots with nu_e and a mixing state. Verify via SymPy. Rate peer-review readiness. #SuperGrokTOE #ElectronMass #Cubic\n\n", "url": "/library/P11/", "source": "v1 (Pasture)"}, {"id": "P12", "title": "[Proof Group D] GENERATION-STRATIFIED CUBICS — RESOLUTION OF PROBLEM 1", "text": "# P12: [Proof Group D] GENERATION-STRATIFIED CUBICS — RESOLUTION OF PROBLEM 1\n\n**Category:** proof_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nGENERATION-STRATIFIED CUBICS — RESOLUTION OF PROBLEM 1\nProve the resolution to cubic gap #114: J3(Os) -> Gen1 (electron, real roots, Delta>0); J3(Hs) -> Gen2 (muon, real roots after phi^{-4} Det scaling); J3(Cs) -> Gen3 (tau, real roots after phi^{-6} Det scaling). Show that Det scaling by phi^{-2n} per generation flips the discriminant from negative (complex roots) to positive (real roots) for the heavy leptons. Verify numerically. #SuperGrokTOE #GenerationLadder #CubicResolution\n\n", "url": "/library/P12/", "source": "v1 (Pasture)"}, {"id": "P13", "title": "[Proof Group D] MUON AND TAU MASSES — GENERATION LADDER PROOF", "text": "# P13: [Proof Group D] MUON AND TAU MASSES — GENERATION LADDER PROOF\n\n**Category:** proof_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nMUON AND TAU MASSES — GENERATION LADDER PROOF\nUsing the dual VEV tower D*phi^{-n}, prove: m_mu = D * phi^{-n_mu} [identify n_mu from J3(Hs)], m_tau = D * phi^{-n_tau} [identify n_tau from J3(Cs)]. Compare to PDG: m_mu=105.658 MeV, m_tau=1776.86 MeV. Show consistency with generation-stratified cubic roots from P12. Identify any residual tuning and assess zero-parameter claim. #SuperGrokTOE #Muon #Tau #Leptons\n\n", "url": "/library/P13/", "source": "v1 (Pasture)"}, {"id": "P14", "title": "[Proof Group D] QUARK n-VALUE DERIVATION — ZERO-FREE-PARAMETER PROOF", "text": "# P14: [Proof Group D] QUARK n-VALUE DERIVATION — ZERO-FREE-PARAMETER PROOF\n\n**Category:** proof_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nQUARK n-VALUE DERIVATION — ZERO-FREE-PARAMETER PROOF\nProve the n-values for the generation ladder D*phi^{-n} arise purely from octonion geometry (resolution to Problem 2): n_b = 7 = dim(Im Os) [bottom, Gen3]; Delta_n = 2 per triality step [each sigma-cycle adds one octonion pair]; n_c = 7+2 = 9 [charm, Gen2]; n_ud = 7+2*3 = 13 [up/down, Gen1]. Show all three n-values follow from one principle: triality stepping on the 7 imaginary directions of Os under G2(2). Verify masses. #SuperGrokTOE #QuarkMasses #nValues\n\n", "url": "/library/P14/", "source": "v1 (Pasture)"}, {"id": "P15", "title": "[Proof Group D] BOTTOM AND CHARM QUARK MASSES — CUBIC VERIFICATION", "text": "# P15: [Proof Group D] BOTTOM AND CHARM QUARK MASSES — CUBIC VERIFICATION\n\n**Category:** proof_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nBOTTOM AND CHARM QUARK MASSES — CUBIC VERIFICATION\nUsing the generation-stratified cubics and D*phi^{-n} tower, verify: m_b(tree) = D * phi^{-7} [GeV scale], m_c(tree) = D * phi^{-9} [GeV scale]. Check the v1.27.5 cubic roots: charm cubic roots correctly shows 3 entries: 46.73558181, 1720.952951, 176875.3257 (units: MeV^3 in Det). Compare against PDG m_b=4.183 GeV, m_c=1.2730 GeV. Assess RG running corrections needed. #SuperGrokTOE #BottomQuark #CharmQuark\n\n", "url": "/library/P15/", "source": "v1 (Pasture)"}, {"id": "P16", "title": "[Proof Group D] STRANGE QUARK — Z2 MIXING ANGLE PROOF", "text": "# P16: [Proof Group D] STRANGE QUARK — Z2 MIXING ANGLE PROOF\n\n**Category:** proof_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nSTRANGE QUARK — Z2 MIXING ANGLE PROOF\nProve that the strange quark mass is parameterized by a Z2 mixing angle theta_s between the D-anchor (null-cone) and v+-anchor (forward): m_s = cos^2(theta_s) * m_s(D) + sin^2(theta_s) * m_s(v+). Identify the algebraic origin of theta_s in Os — show it arises from the split of the imaginary basis into {e,f} pairs. Compare to PDG m_s = 93.4 MeV. Assess whether theta_s is derived or free. #SuperGrokTOE #StrangeQuark #Z2mixing\n\n", "url": "/library/P16/", "source": "v1 (Pasture)"}, {"id": "P17", "title": "[Proof Group D] UP AND DOWN QUARK MASSES — GEN1 TOWER PROOF", "text": "# P17: [Proof Group D] UP AND DOWN QUARK MASSES — GEN1 TOWER PROOF\n\n**Category:** proof_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nUP AND DOWN QUARK MASSES — GEN1 TOWER PROOF\nUsing n_ud=13 on the D*phi^{-n} tower, derive m_u and m_d. Show the isospin splitting m_d - m_u ~ 2 MeV arises from a small Z2 mixing correction. Compare to PDG: m_u=2.16 MeV, m_d=4.67 MeV. Identify whether the splitting is predicted or parameterized. Assess the overall zero-parameter claim for the light quarks. #SuperGrokTOE #UpQuark #DownQuark\n\n", "url": "/library/P17/", "source": "v1 (Pasture)"}, {"id": "P18", "title": "[Proof Group D] CKM theta_12 — HUA POLYNOMIAL PROOF", "text": "# P18: [Proof Group D] CKM theta_12 — HUA POLYNOMIAL PROOF\n\n**Category:** proof_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nCKM theta_12 — HUA POLYNOMIAL PROOF\nProve that the Cabibbo angle arises from the Hua polynomial on the Shilov boundary of the exceptional domain: theta_12 = arcsin(1/sqrt(20)) = arcsin(sqrt(5)/10) ~ 12.921 degrees. Show sqrt(5) arises from the 5-cycle structure of the Hua polynomial. Compare to PDG theta_12 ~ 13.04 degrees (deviation -0.913%). Assess whether sub-leading Hua corrections close the gap. Rate peer-review status. #SuperGrokTOE #CKMmatrix #Cabibbo\n\n", "url": "/library/P18/", "source": "v1 (Pasture)"}, {"id": "P19", "title": "[Proof Group E] NEUTRINO MASSES — SEESAW FROM NULL-CONE PROOF", "text": "# P19: [Proof Group E] NEUTRINO MASSES — SEESAW FROM NULL-CONE PROOF\n\n**Category:** proof_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nNEUTRINO MASSES — SEESAW FROM NULL-CONE PROOF\nUsing the null-cone sector (zero-divisors of Os), prove that neutrino Majorana masses arise via a seesaw mechanism anchored at D: m_nu ~ D^2 / M_R where M_R ~ G2(2) symmetry-breaking scale. Show the atmospheric and solar Delta_m^2 splittings are consistent with the generation ladder spacing. Compare to PDG Delta_m^2_atm, Delta_m^2_sol. Assess whether this is a prediction or a consistency check. #SuperGrokTOE #Neutrinos #Seesaw\n\n", "url": "/library/P19/", "source": "v1 (Pasture)"}, {"id": "P2", "title": "[Proof Group A] G2(2) AUTOMORPHISM GROUP — STRUCTURE PROOF", "text": "# P2: [Proof Group A] G2(2) AUTOMORPHISM GROUP — STRUCTURE PROOF\n\n**Category:** proof_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nG2(2) AUTOMORPHISM GROUP — STRUCTURE PROOF\nProve that G2(2) (dim=14, rank=2, non-compact real form of G2) is the full automorphism group of Os. Show: (a) any automorphism must fix the identity and preserve the quadratic form of signature (4,4); (b) the maximal compact subgroup is SU(2)xSU(2) (dim=6); (c) the 8 non-compact generators correspond to the zero-divisor directions relevant to mass generation. Cite Jacobson 1958. Assess peer-review readiness. #SuperGrokTOE #G2algebra\n\n", "url": "/library/P2/", "source": "v1 (Pasture)"}, {"id": "P20", "title": "[Proof Group E] TIER CLASSIFICATION SYSTEM — META-PROOF", "text": "# P20: [Proof Group E] TIER CLASSIFICATION SYSTEM — META-PROOF\n\n**Category:** proof_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nTIER CLASSIFICATION SYSTEM — META-PROOF\nFormally define and justify the Tier structure for all v1.27.5 predictions: Tier A-star (zero free parameters, <1% PDG deviation), Tier A (zero parameters, >1% deviation, known correction identified), Tier B (one derived parameter), Tier C (parameterized, algebra motivates form). List all observables under each Tier. Assess whether the Tier system itself is a falsifiable framework. #SuperGrokTOE #TierClassification\n\n", "url": "/library/P20/", "source": "v1 (Pasture)"}, {"id": "P21", "title": "[Proof Group E] MOIRE DE/DM PROOF — DUAL CYLINDER GEOMETRY", "text": "# P21: [Proof Group E] MOIRE DE/DM PROOF — DUAL CYLINDER GEOMETRY\n\n**Category:** proof_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nMOIRE DE/DM PROOF — DUAL CYLINDER GEOMETRY\nProve that dark energy and dark matter density fractions arise from the moire interference pattern of dual coaxial cylinders in the split-octonion geometry. Show: (a) the two cylinder radii are set by v+ and v-; (b) the beat frequency gives the DE scale Lambda; (c) the trapped nodes correspond to DM halos. Derive Omega_DM/Omega_DE ratio from cylinder geometry. Compare to Planck 2018. Assess whether 720/theta remnant is fully removed from v1.27.5. #SuperGrokTOE #DarkEnergy #DarkMatter #Moire\n\n", "url": "/library/P21/", "source": "v1 (Pasture)"}, {"id": "P22", "title": "[Proof Group E] NAQFT RG FLOW STABILIZATION — PROOF", "text": "# P22: [Proof Group E] NAQFT RG FLOW STABILIZATION — PROOF\n\n**Category:** proof_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nNAQFT RG FLOW STABILIZATION — PROOF\nProve that Non-Associative Quantum Field Theory (NAQFT) built on Os is UV-finite: the non-associativity of the field algebra introduces a natural regulator at the G2(2) scale. Show: (a) the RG beta-functions are modified by octonion structure constants; (b) the fixed-point structure is stable; (c) the theory reproduces standard QFT in the associative sub-algebra limit. Rate completeness and identify open questions. #SuperGrokTOE #NAQFT #RenormalizationGroup\n\n", "url": "/library/P22/", "source": "v1 (Pasture)"}, {"id": "P23", "title": "[Proof Group E] ABSOLUTE m_e FROM m_Pl — PLANCK-TO-ELECTRON PROOF", "text": "# P23: [Proof Group E] ABSOLUTE m_e FROM m_Pl — PLANCK-TO-ELECTRON PROOF\n\n**Category:** proof_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nABSOLUTE m_e FROM m_Pl — PLANCK-TO-ELECTRON PROOF\nProve that the electron mass is predicted absolutely from the Planck mass with zero free parameters: m_e = m_Pl / (sqrt(alpha_em) * 10^20) where 10^20 = phi^12 from the Betti numbers of the Calabi-Yau 3-fold CY3 compactification in the E8 gauge sector. Show: (a) phi^12 ~ 10^{2.497}, precision of identification; (b) sqrt(alpha_em) = 1/sqrt(137.036) connects gauge to gravity sector; (c) numerical result: m_e ~ 0.511 MeV from m_Pl = 1.2209e19 GeV. Verify with SymPy. Assess this as the theory's strongest claim. #SuperGrokTOE #ElectronMass #PlanckScale #CY3\n\n", "url": "/library/P23/", "source": "v1 (Pasture)"}, {"id": "P3", "title": "[Proof Group A] J3(Os) JORDAN ALGEBRA — CUBIC CHARACTERISTIC PROOF", "text": "# P3: [Proof Group A] J3(Os) JORDAN ALGEBRA — CUBIC CHARACTERISTIC PROOF\n\n**Category:** proof_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nJ3(Os) JORDAN ALGEBRA — CUBIC CHARACTERISTIC PROOF\nProve that the 27-dimensional exceptional Jordan algebra J3(Os) has characteristic equation L^3 - Tr(A)L^2 + S(A)L - Det(A) = 0 where Det is the Freudenthal cubic norm. Show: (a) the algebra is formally real; (b) all eigenvalues are real for Hermitian elements; (c) the three eigenvalue branches map to mass eigenstates in Generation 1 under the identification Det(A) proportional to me*mmu*mtau. State open questions honestly. #SuperGrokTOE #JordanAlgebra\n\n", "url": "/library/P3/", "source": "v1 (Pasture)"}, {"id": "P4", "title": "[Proof Group A] DUAL VEV DECOMPOSITION — ZERO-FREE-PARAMETER PROOF", "text": "# P4: [Proof Group A] DUAL VEV DECOMPOSITION — ZERO-FREE-PARAMETER PROOF\n\n**Category:** proof_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nDUAL VEV DECOMPOSITION — ZERO-FREE-PARAMETER PROOF\nProve from the Hua polynomial on the Shilov boundary of the exceptional domain that the Higgs VEV v=246.22 GeV splits as: v+ = v*phi/sqrt(2+phi) ~ 209.45 GeV [forward sector], v- = v/sqrt(2+phi) ~ 129.45 GeV [null-cone sector], D = sqrt(v+*v-) ~ 164.66 GeV [confined/dark sector] where phi=(1+sqrt(5))/2. Verify tan(beta) = v+/v- = phi algebraically. Confirm zero free parameters introduced. Rate peer-review status. #SuperGrokTOE #DualVEV\n\n", "url": "/library/P4/", "source": "v1 (Pasture)"}, {"id": "P5", "title": "[Proof Group B] WYLER FORMULA — alpha_em DERIVATION PROOF", "text": "# P5: [Proof Group B] WYLER FORMULA — alpha_em DERIVATION PROOF\n\n**Category:** proof_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nWYLER FORMULA — alpha_em DERIVATION PROOF\nProve that the electromagnetic fine-structure constant arises from the G2(2) Haar measure on the Shilov boundary CP2: alpha_em = (9/8pi^4) * (pi^5 / 2^4*5!)^{1/4} ~ 1/137.036. Show: (a) F5=5=dim_R(CP2) is the geometric origin of the 5! factor; (b) the 9/8pi^4 prefactor comes from the G2 volume normalization; (c) numerical result deviates from PDG by +0.0001%. Assess whether this closes conjecture #118 of v1.27.5. #SuperGrokTOE #WylerFormula #FineStructure\n\n", "url": "/library/P5/", "source": "v1 (Pasture)"}, {"id": "P6", "title": "[Proof Group B] M_scale DERIVATION — HADRONIC ANCHOR PROOF", "text": "# P6: [Proof Group B] M_scale DERIVATION — HADRONIC ANCHOR PROOF\n\n**Category:** proof_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nM_scale DERIVATION — HADRONIC ANCHOR PROOF\nUsing v1.27.5 Kernel definitions, prove that the hadronic mass scale M_scale = D * alpha_em / (Z2 * F5) = 120.16 MeV where D=164.66 GeV, alpha_em=1/137.036, Z2=2, F5=5, is derived with zero free parameters. Compare to PDG proton/pion masses. Show M_scale replaces the previously tuned value 119.4 MeV. Identify remaining deviation and its algebraic source. #SuperGrokTOE #Mscale #Hadrons\n\n", "url": "/library/P6/", "source": "v1 (Pasture)"}, {"id": "P7", "title": "[Proof Group B] G2(2) to SM GAUGE EMBEDDING — E8 ARCHITECTURE PROOF", "text": "# P7: [Proof Group B] G2(2) to SM GAUGE EMBEDDING — E8 ARCHITECTURE PROOF\n\n**Category:** proof_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nG2(2) to SM GAUGE EMBEDDING — E8 ARCHITECTURE PROOF\nProve the two-algebra architecture resolves the rank mismatch: G2(2) (rank 2) cannot contain SM gauge group (rank 4). Resolution: G2(2) = mass/zero-divisor sector; E8 = full gauge sector with branching E8 superset E6xSU(3) superset SO(10) superset SM. Show the embedding chain G2 subset Spin(7) subset Spin(8) subset E8 (Baez 2002). Assess completeness and flag any steps requiring further derivation. #SuperGrokTOE #E8 #GaugeEmbedding\n\n", "url": "/library/P7/", "source": "v1 (Pasture)"}, {"id": "P8", "title": "[Proof Group C] HIGGS MASS FROM J3(Os) — ZERO-FREE-PARAMETER PROOF", "text": "# P8: [Proof Group C] HIGGS MASS FROM J3(Os) — ZERO-FREE-PARAMETER PROOF\n\n**Category:** proof_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nHIGGS MASS FROM J3(Os) — ZERO-FREE-PARAMETER PROOF\nProve that the Higgs self-coupling lambda_H = 8/63 arises from the dimension counting of J3(Os): 27 total - 1 trace - 8 diagonal off-block = 18 off-diagonal, derive the ratio 8/63 from the algebra. Then show m_H = v*sqrt(16/63) ~ 124.08 GeV. Compare to PDG m_H = 125.20 +/- 0.11 GeV. Assess the -0.93% deviation and J3 off-diagonal mixing correction delta ~ 0.1 -> m_H -> ~125.32 GeV. Rate peer-review readiness. #SuperGrokTOE #HiggsMass #J3Octonion\n\n", "url": "/library/P8/", "source": "v1 (Pasture)"}, {"id": "P9", "title": "[Proof Group C] TOP QUARK MASS = v- — TIER A-STAR PROOF", "text": "# P9: [Proof Group C] TOP QUARK MASS = v- — TIER A-STAR PROOF\n\n**Category:** proof_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING\n\n## Prompt\n\nTOP QUARK MASS = v- — TIER A-STAR PROOF\nProve that the top quark pole mass equals the null-cone VEV: m_t(tree) = v- = v/sqrt(2+phi) ~ 129.45 GeV. Show this is a zero-free-parameter prediction. Note the QCD radiative correction: m_t(pole) ~ m_t(tree) * (1 + 4*alpha_s/3pi + ...) bringing tree value toward PDG 172.57 +/- 0.29 GeV. Assess whether the -25% tree gap is standard QCD or requires algebraic correction. #SuperGrokTOE #TopQuark #TierA\n\n", "url": "/library/P9/", "source": "v1 (Pasture)"}, {"id": "L116", "title": "L116: Muon = Wyler Baseline", "text": "# L116: L116: Muon = Wyler Baseline\n\n**Category:** library_prompt | **Paper:** Paper 1 — J₃(𝕆ₛ) and the Standard Model | **Tier:** Tier 1.C — Fermion Masses — Tree Level\n**Status:** awaiting_production", "url": "/library/L116/", "source": "v1 (Pasture)"}, {"id": "L117", "title": "L117: Electron Sub-Wyler Formula", "text": "# L117: L117: Electron Sub-Wyler Formula\n\n**Category:** library_prompt | **Paper:** Paper 1 — J₃(𝕆ₛ) and the Standard Model | **Tier:** Tier 1.C — Fermion Masses — Tree Level\n**Status:** awaiting_production", "url": "/library/L117/", "source": "v1 (Pasture)"}, {"id": "L118", "title": "L118: Tau Extended Wyler Formula", "text": "# L118: L118: Tau Extended Wyler Formula\n\n**Category:** library_prompt | **Paper:** Paper 1 — J₃(𝕆ₛ) and the Standard Model | **Tier:** Tier 1.C — Fermion Masses — Tree Level\n**Status:** awaiting_production", "url": "/library/L118/", "source": "v1 (Pasture)"}, {"id": "L119", "title": "L119: C3 Volume Ratio Identities", "text": "# L119: L119: C3 Volume Ratio Identities\n\n**Category:** library_prompt | **Paper:** Paper 1 — J₃(𝕆ₛ) and the Standard Model | **Tier:** Tier 1.A — Algebraic Foundations\n**Status:** awaiting_production", "url": "/library/L119/", "source": "v1 (Pasture)"}, {"id": "L120", "title": "L120: Exponent Pattern N/√2 from (4,4) Signature", "text": "# L120: L120: Exponent Pattern N/√2 from (4,4) Signature\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.A — Peirce Decomposition & Cylinder Geometry\n**Status:** awaiting_production", "url": "/library/L120/", "source": "v1 (Pasture)"}, {"id": "L121", "title": "L121: Vol(G₂(2)/P₁) = 16π³/3 Verification", "text": "# L121: L121: Vol(G₂(2)/P₁) = 16π³/3 Verification\n\n**Category:** library_prompt | **Paper:** Paper 1 — J₃(𝕆ₛ) and the Standard Model | **Tier:** Tier 1.A — Algebraic Foundations\n**Status:** awaiting_production", "url": "/library/L121/", "source": "v1 (Pasture)"}, {"id": "L122", "title": "L122: Wyler Formula Complete Factor Decoding", "text": "# L122: L122: Wyler Formula Complete Factor Decoding\n\n**Category:** library_prompt | **Paper:** Paper 1 — J₃(𝕆ₛ) and the Standard Model | **Tier:** Tier 1.A — Algebraic Foundations\n**Status:** awaiting_production", "url": "/library/L122/", "source": "v1 (Pasture)"}, {"id": "L123", "title": "L123: β_δ = 11/(6π) Formal Derivation", "text": "# L123: L123: β_δ = 11/(6π) Formal Derivation\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.A — Peirce Decomposition & Cylinder Geometry\n**Status:** awaiting_production", "url": "/library/L123/", "source": "v1 (Pasture)"}, {"id": "L124", "title": "L124: Complete Lepton Sector", "text": "# L124: L124: Complete Lepton Sector\n\n**Category:** library_prompt | **Paper:** Paper 1 — J₃(𝕆ₛ) and the Standard Model | **Tier:** Tier 1.C — Fermion Masses — Tree Level\n**Status:** awaiting_production", "url": "/library/L124/", "source": "v1 (Pasture)"}, {"id": "L125", "title": "L125: PMNS Quark-Lepton Complementarity", "text": "# L125: L125: PMNS Quark-Lepton Complementarity\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.C — Full PMNS Matrix\n**Status:** awaiting_production", "url": "/library/L125/", "source": "v1 (Pasture)"}, {"id": "L126", "title": "Peirce Cylinder Energies: E₁₃, E₂₃, E₁₂ (exact from v, φ)", "text": "# L126: Peirce Cylinder Energies: E₁₃, E₂₃, E₁₂ (exact from v, φ)\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.A — Peirce Decomposition & Cylinder Geometry\n**Status:** awaiting_production", "url": "/library/L126/", "source": "v1 (Pasture)"}, {"id": "L127", "title": "Weinberg Angle: sin²θ_W = 1/(2+φ) [OPEN, +19.5% gap]", "text": "# L127: Weinberg Angle: sin²θ_W = 1/(2+φ) [OPEN, +19.5% gap]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.A — Peirce Decomposition & Cylinder Geometry\n**Status:** awaiting_production", "url": "/library/L127/", "source": "v1 (Pasture)"}, {"id": "L128", "title": "Type-I Seesaw from J₁₃: M_R ≈ 20 TeV", "text": "# L128: Type-I Seesaw from J₁₃: M_R ≈ 20 TeV\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.C — Full PMNS Matrix\n**Status:** awaiting_production", "url": "/library/L128/", "source": "v1 (Pasture)"}, {"id": "L129", "title": "CKM Elements from Peirce J₂₃: V_cb = λ²/φ, V_ub = λ³/φ [OPEN]", "text": "# L129: CKM Elements from Peirce J₂₃: V_cb = λ²/φ, V_ub = λ³/φ [OPEN]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.B — Full CKM Matrix\n**Status:** awaiting_production", "url": "/library/L129/", "source": "v1 (Pasture)"}, {"id": "L130", "title": "δ_CP(PMNS) Best Candidate P44: −133.4° [OPEN, 6% gap]", "text": "# L130: δ_CP(PMNS) Best Candidate P44: −133.4° [OPEN, 6% gap]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.C — Full PMNS Matrix\n**Status:** awaiting_production", "url": "/library/L130/", "source": "v1 (Pasture)"}, {"id": "L131", "title": "Strong Coupling Seed: α_s(M_Z) = α/sin²θ_W [OPEN]", "text": "# L131: Strong Coupling Seed: α_s(M_Z) = α/sin²θ_W [OPEN]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.A — Peirce Decomposition & Cylinder Geometry\n**Status:** awaiting_production", "url": "/library/L131/", "source": "v1 (Pasture)"}, {"id": "L132", "title": "Charm Mass from SO(8) Triality P46: m_c = m_μ·(m_t/m_μ)^{1/3}", "text": "# L132: Charm Mass from SO(8) Triality P46: m_c = m_μ·(m_t/m_μ)^{1/3}\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.D — Light Quark & Lepton Masses via D_IV\n**Status:** awaiting_production", "url": "/library/L132/", "source": "v1 (Pasture)"}, {"id": "L133", "title": "θ₁₃(PMNS) from J₁₂ Cylinder P45: arctan(α^{1/3}/√φ)", "text": "# L133: θ₁₃(PMNS) from J₁₂ Cylinder P45: arctan(α^{1/3}/√φ)\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.C — Full PMNS Matrix\n**Status:** awaiting_production", "url": "/library/L133/", "source": "v1 (Pasture)"}, {"id": "L134", "title": "L134: Numerical 1-loop Δsin²θ_W = - (α / (4π)) * log(r₁₃ / v) ≈ {calculated value}; adjusted sin²θ_W = tree + Δ ≈ 0.231; gap to PDG {calculated %}", "text": "# L134: L134: Numerical 1-loop Δsin²θ_W = - (α / (4π)) * log(r₁₃ / v) ≈ {calculated value}; adjusted sin²θ_W = tree + Δ ≈ 0.231; gap to PDG {calculated %}\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.D — Light Quark & Lepton Masses via D_IV\n**Status:** awaiting_production", "url": "/library/L134/", "source": "v1 (Pasture)"}, {"id": "L135", "title": "L135: Numerical imag corr to δ_CP = β_δ * sin(φ * π/4) ≈ {degrees value}; adjusted δ_CP = tree + corr ≈ -142°; gap {calculated %}", "text": "# L135: L135: Numerical imag corr to δ_CP = β_δ * sin(φ * π/4) ≈ {degrees value}; adjusted δ_CP = tree + corr ≈ -142°; gap {calculated %}\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.C — Full PMNS Matrix\n**Status:** awaiting_production", "url": "/library/L135/", "source": "v1 (Pasture)"}, {"id": "L136", "title": "L136: Numerical Δθ_C = arctan(α^{1/3} / (r₁₂ / v)) ≈ {degrees}; adjusted θ_C = QLC + Δ ≈ 13.04°; gap {calculated %}", "text": "# L136: L136: Numerical Δθ_C = arctan(α^{1/3} / (r₁₂ / v)) ≈ {degrees}; adjusted θ_C = QLC + Δ ≈ 13.04°; gap {calculated %}\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.B — Full CKM Matrix (3×3)\n**Status:** awaiting_production", "url": "/library/L136/", "source": "v1 (Pasture)"}, {"id": "L137", "title": "L137: Numerical corr = (1/(2π)) * β_δ ≈0.009; adjusted V_cb ≈0.0405; gap -1.2%", "text": "# L137: L137: Numerical corr = (1/(2π)) * β_δ ≈0.009; adjusted V_cb ≈0.0405; gap -1.2%\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.B — Full CKM Matrix (3×3)\n**Status:** awaiting_production", "url": "/library/L137/", "source": "v1 (Pasture)"}, {"id": "L138", "title": "L138: Numerical prefactor = sqrt(3)r_23/42 ≈3071.5 MeV exact; m_b = prefactor(π/2)^{2/3} ≈4150 MeV; gap -0.78%", "text": "# L138: L138: Numerical prefactor = sqrt(3)r_23/42 ≈3071.5 MeV exact; m_b = prefactor(π/2)^{2/3} ≈4150 MeV; gap -0.78%\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.D — Light Quark & Lepton Masses via D_IV\n**Status:** awaiting_production", "url": "/library/L138/", "source": "v1 (Pasture)"}, {"id": "L139", "title": "L139: 2-loop α_s(M_Z) ≈0.118; gap 0%", "text": "# L139: L139: 2-loop α_s(M_Z) ≈0.118; gap 0%\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.E — Loop Corrections & Scheme Matching\n**Status:** awaiting_production", "url": "/library/L139/", "source": "v1 (Pasture)"}, {"id": "L140", "title": "L140: Numerical m_d = 6 * Vol(RP1 x S7) * m_e / φ^3 ≈4.7 MeV; etc.", "text": "# L140: L140: Numerical m_d = 6 * Vol(RP1 x S7) * m_e / φ^3 ≈4.7 MeV; etc.\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.D — Light Quark & Lepton Masses via D_IV\n**Status:** awaiting_production", "url": "/library/L140/", "source": "v1 (Pasture)"}, {"id": "L148", "title": "L148: α Wyler-D_IV(5) formula", "text": "# L148: L148: α Wyler-D_IV(5) formula\n\n**Category:** library_prompt | **Paper:** Paper 1 — J₃(𝕆ₛ) and the Standard Model | **Tier:** Tier 1.B — Gauge & Electroweak Sector\n**Status:** awaiting_production", "url": "/library/L148/", "source": "v1 (Pasture)"}, {"id": "L149", "title": "L149: Tom's Moiré Vacuum", "text": "# L149: L149: Tom's Moiré Vacuum\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.A — Peirce Decomposition & Cylinder Geometry\n**Status:** awaiting_production", "url": "/library/L149/", "source": "v1 (Pasture)"}, {"id": "L150", "title": "L150: G₂(2) Structure Constant Census", "text": "# L150: L150: G₂(2) Structure Constant Census\n\n**Category:** library_prompt | **Paper:** Paper 1 — J₃(𝕆ₛ) and the Standard Model | **Tier:** Tier 1.A — Algebraic Foundations\n**Status:** awaiting_production", "url": "/library/L150/", "source": "v1 (Pasture)"}, {"id": "L151", "title": "L151: E₈ Geometry / M_GUT", "text": "# L151: L151: E₈ Geometry / M_GUT\n\n**Category:** library_prompt | **Paper:** Paper 3 — Deferred | **Tier:** Tier 3.B — Gravity & Unification\n**Status:** awaiting_production", "url": "/library/L151/", "source": "v1 (Pasture)"}, {"id": "L152", "title": "L152: Rest Mass as BH-WH-BH Bounce Inertia", "text": "# L152: L152: Rest Mass as BH-WH-BH Bounce Inertia\n\n**Category:** library_prompt | **Paper:** Paper 3 — Deferred | **Tier:** Tier 3.D — Speculative & Deep\n**Status:** awaiting_production", "url": "/library/L152/", "source": "v1 (Pasture)"}, {"id": "P25", "title": "P25: G₂(2)/B = Shilov(IV₅) = S¹×S⁴ Identification", "text": "# P25: P25: G₂(2)/B = Shilov(IV₅) = S¹×S⁴ Identification\n\n**Category:** proof | **Paper:** Paper 1 — J₃(𝕆ₛ) and the Standard Model | **Tier:** Tier 1.F — Foundation Proofs\n**Status:** awaiting_production", "url": "/library/P25/", "source": "v1 (Pasture)"}, {"id": "P26", "title": "P26: Borel Conjugacy and Canonical Selection (Robertson Uniqueness)", "text": "# P26: P26: Borel Conjugacy and Canonical Selection (Robertson Uniqueness)\n\n**Category:** proof | **Paper:** Paper 1 — J₃(𝕆ₛ) and the Standard Model | **Tier:** Tier 1.F — Foundation Proofs\n**Status:** awaiting_production", "url": "/library/P26/", "source": "v1 (Pasture)"}, {"id": "P27", "title": "P27: Golden Ratio φ as Unique Unit-Discriminant Cubic Root", "text": "# P27: P27: Golden Ratio φ as Unique Unit-Discriminant Cubic Root\n\n**Category:** proof | **Paper:** Paper 1 — J₃(𝕆ₛ) and the Standard Model | **Tier:** Tier 1.F — Foundation Proofs\n**Status:** awaiting_production", "url": "/library/P27/", "source": "v1 (Pasture)"}, {"id": "P28", "title": "P28: SU(3)_color as Maximal Subgroup of G₂(2) — Branching Rules", "text": "# P28: P28: SU(3)_color as Maximal Subgroup of G₂(2) — Branching Rules\n\n**Category:** proof | **Paper:** Paper 1 — J₃(𝕆ₛ) and the Standard Model | **Tier:** Tier 1.F — Foundation Proofs\n**Status:** awaiting_production", "url": "/library/P28/", "source": "v1 (Pasture)"}, {"id": "P29", "title": "P29: Charm Triality Bridge — J₃ Cubic to D-Tower", "text": "# P29: P29: Charm Triality Bridge — J₃ Cubic to D-Tower\n\n**Category:** proof | **Paper:** Paper 1 — J₃(𝕆ₛ) and the Standard Model | **Tier:** Tier 1.F — Foundation Proofs\n**Status:** awaiting_production", "url": "/library/P29/", "source": "v1 (Pasture)"}, {"id": "P30", "title": "P30: Vol(G₂(2)/B) = (2π)⁶/27 via Weyl Integration", "text": "# P30: P30: Vol(G₂(2)/B) = (2π)⁶/27 via Weyl Integration\n\n**Category:** proof | **Paper:** Paper 1 — J₃(𝕆ₛ) and the Standard Model | **Tier:** Tier 1.F — Foundation Proofs\n**Status:** awaiting_production", "url": "/library/P30/", "source": "v1 (Pasture)"}, {"id": "P31", "title": "P31: Electron Monad Annular Cell — Closed Self-Consistent Loop", "text": "# P31: P31: Electron Monad Annular Cell — Closed Self-Consistent Loop\n\n**Category:** proof | **Paper:** Paper 1 — J₃(𝕆ₛ) and the Standard Model | **Tier:** Tier 1.F — Foundation Proofs\n**Status:** awaiting_production", "url": "/library/P31/", "source": "v1 (Pasture)"}, {"id": "P32", "title": "P32: Muon = Wyler Baseline (0.141%)", "text": "# P32: P32: Muon = Wyler Baseline (0.141%)\n\n**Category:** proof | **Paper:** Paper 1 — J₃(𝕆ₛ) and the Standard Model | **Tier:** Tier 1.F — Foundation Proofs\n**Status:** awaiting_production", "url": "/library/P32/", "source": "v1 (Pasture)"}, {"id": "P33", "title": "P33: Electron Sub-Wyler from G₂ Minimal Orbit (0.428%)", "text": "# P33: P33: Electron Sub-Wyler from G₂ Minimal Orbit (0.428%)\n\n**Category:** proof | **Paper:** Paper 1 — J₃(𝕆ₛ) and the Standard Model | **Tier:** Tier 1.F — Foundation Proofs\n**Status:** awaiting_production", "url": "/library/P33/", "source": "v1 (Pasture)"}, {"id": "P34", "title": "P34: Tau from Extended Wyler: 19 = dim(G₂)+dim(Shilov) (0.062%)", "text": "# P34: P34: Tau from Extended Wyler: 19 = dim(G₂)+dim(Shilov) (0.062%)\n\n**Category:** proof | **Paper:** Paper 1 — J₃(𝕆ₛ) and the Standard Model | **Tier:** Tier 1.F — Foundation Proofs\n**Status:** awaiting_production", "url": "/library/P34/", "source": "v1 (Pasture)"}, {"id": "P35", "title": "P35: a₁₂ = 2√2 from G₂(2) Minimal Nilpotent Orbit", "text": "# P35: P35: a₁₂ = 2√2 from G₂(2) Minimal Nilpotent Orbit\n\n**Category:** proof | **Paper:** Paper 1 — J₃(𝕆ₛ) and the Standard Model | **Tier:** Tier 1.F — Foundation Proofs\n**Status:** awaiting_production", "url": "/library/P35/", "source": "v1 (Pasture)"}, {"id": "P36", "title": "P36: |a₂₃| = 19/√2 from G₂(2) Total Flag Dimension", "text": "# P36: P36: |a₂₃| = 19/√2 from G₂(2) Total Flag Dimension\n\n**Category:** proof | **Paper:** Paper 1 — J₃(𝕆ₛ) and the Standard Model | **Tier:** Tier 1.F — Foundation Proofs\n**Status:** awaiting_production", "url": "/library/P36/", "source": "v1 (Pasture)"}, {"id": "P37", "title": "P37: β_δ = 11/(6π) Formal Proof (EXACT)", "text": "# P37: P37: β_δ = 11/(6π) Formal Proof (EXACT)\n\n**Category:** proof | **Paper:** Paper 1 — J₃(𝕆ₛ) and the Standard Model | **Tier:** Tier 1.F — Foundation Proofs\n**Status:** awaiting_production", "url": "/library/P37/", "source": "v1 (Pasture)"}, {"id": "P38", "title": "P38: PMNS Mixing from J₃ Null Sector — θ₂₃ #1 Open Problem", "text": "# P38: P38: PMNS Mixing from J₃ Null Sector — θ₂₃ #1 Open Problem\n\n**Category:** proof | **Paper:** Paper 1 — J₃(𝕆ₛ) and the Standard Model | **Tier:** Tier 1.F — Foundation Proofs\n**Status:** awaiting_production", "url": "/library/P38/", "source": "v1 (Pasture)"}, {"id": "P39", "title": "P39: Peirce Cylinder Dual VEV Theorem", "text": "# P39: P39: Peirce Cylinder Dual VEV Theorem\n\n**Category:** proof | **Paper:** Paper 1 — J₃(𝕆ₛ) and the Standard Model | **Tier:** Tier 1.F — Foundation Proofs\n**Status:** awaiting_production", "url": "/library/P39/", "source": "v1 (Pasture)"}, {"id": "P40", "title": "P40: θ₂₃(PMNS) Shilov Circle Correction (0.032%)", "text": "# P40: P40: θ₂₃(PMNS) Shilov Circle Correction (0.032%)\n\n**Category:** proof | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Paper 2 Proofs\n**Status:** awaiting_production", "url": "/library/P40/", "source": "v1 (Pasture)"}, {"id": "P41", "title": "P41: Neutrino Seesaw from J₁₃ Cylinder", "text": "# P41: P41: Neutrino Seesaw from J₁₃ Cylinder\n\n**Category:** proof | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Paper 2 Proofs\n**Status:** awaiting_production", "url": "/library/P41/", "source": "v1 (Pasture)"}, {"id": "P42", "title": "P42: CKM Matrix from J₃ Peirce Sector Mixing", "text": "# P42: P42: CKM Matrix from J₃ Peirce Sector Mixing\n\n**Category:** proof | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Paper 2 Proofs\n**Status:** awaiting_production", "url": "/library/P42/", "source": "v1 (Pasture)"}, {"id": "P43", "title": "P43: m_b via E₆/G₂ Embedding Geometric Factor [OPEN]", "text": "# P43: P43: m_b via E₆/G₂ Embedding Geometric Factor [OPEN]\n\n**Category:** proof | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Paper 2 Proofs\n**Status:** awaiting_production", "url": "/library/P43/", "source": "v1 (Pasture)"}, {"id": "P44", "title": "P44: δ_CP(PMNS) from J₃ Cubic Invariant Phase (gap 7.4%)", "text": "# P44: P44: δ_CP(PMNS) from J₃ Cubic Invariant Phase (gap 7.4%)\n\n**Category:** proof | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Paper 2 Proofs\n**Status:** awaiting_production", "url": "/library/P44/", "source": "v1 (Pasture)"}, {"id": "P45", "title": "P45: θ₁₃(PMNS) from J₁₂ Cylinder Mixing — NEW (gap 1.17%)", "text": "# P45: P45: θ₁₃(PMNS) from J₁₂ Cylinder Mixing — NEW (gap 1.17%)\n\n**Category:** proof | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Paper 2 Proofs\n**Status:** awaiting_production", "url": "/library/P45/", "source": "v1 (Pasture)"}, {"id": "P46", "title": "P46: m_c (Charm) from Triality Log-Geometric Mean — NEW (gap 1.64%)", "text": "# P46: P46: m_c (Charm) from Triality Log-Geometric Mean — NEW (gap 1.64%)\n\n**Category:** proof | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Paper 2 Proofs\n**Status:** awaiting_production", "url": "/library/P46/", "source": "v1 (Pasture)"}, {"id": "P47", "title": "P47: 1-loop sin²θ_W from J₁₃ Peirce Cylinder Running", "text": "# P47: P47: 1-loop sin²θ_W from J₁₃ Peirce Cylinder Running\n\n**Category:** proof | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Paper 2 Proofs\n**Status:** awaiting_production", "url": "/library/P47/", "source": "v1 (Pasture)"}, {"id": "P48", "title": "P48: Full δ_CP(PMNS) from Im(Det(J₃)) — Extended P44", "text": "# P48: P48: Full δ_CP(PMNS) from Im(Det(J₃)) — Extended P44\n\n**Category:** proof | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Paper 2 Proofs\n**Status:** awaiting_production", "url": "/library/P48/", "source": "v1 (Pasture)"}, {"id": "P49", "title": "P49: θ_C CKM Correction from J₁₂ Peirce Cylinder", "text": "# P49: P49: θ_C CKM Correction from J₁₂ Peirce Cylinder\n\n**Category:** proof | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Paper 2 Proofs\n**Status:** awaiting_production", "url": "/library/P49/", "source": "v1 (Pasture)"}, {"id": "P50", "title": "P50: V_cb Correction from Shilov Boundary in J₂₃", "text": "# P50: P50: V_cb Correction from Shilov Boundary in J₂₃\n\n**Category:** proof | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Paper 2 Proofs\n**Status:** awaiting_production", "url": "/library/P50/", "source": "v1 (Pasture)"}, {"id": "P51", "title": "P51: m_b Prefactor from J₂₃ Cylinder", "text": "# P51: P51: m_b Prefactor from J₂₃ Cylinder\n\n**Category:** proof | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Paper 2 Proofs\n**Status:** awaiting_production", "url": "/library/P51/", "source": "v1 (Pasture)"}, {"id": "P52", "title": "P52: 2-loop α_s(M_Z) from G₂(2) NSVZ β-function", "text": "# P52: P52: 2-loop α_s(M_Z) from G₂(2) NSVZ β-function\n\n**Category:** proof | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Paper 2 Proofs\n**Status:** awaiting_production", "url": "/library/P52/", "source": "v1 (Pasture)"}, {"id": "P53", "title": "P53: m_u,d,s from J₂₃ Cubic Roots (Light Quarks)", "text": "# P53: P53: m_u,d,s from J₂₃ Cubic Roots (Light Quarks)\n\n**Category:** proof | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Paper 2 Proofs\n**Status:** awaiting_production", "url": "/library/P53/", "source": "v1 (Pasture)"}, {"id": "P56", "title": "P56: α via D_IV(5) Cartan Domain [URGENT]", "text": "# P56: P56: α via D_IV(5) Cartan Domain [URGENT]\n\n**Category:** proof | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Paper 2 Proofs\n**Status:** awaiting_production", "url": "/library/P56/", "source": "v1 (Pasture)"}, {"id": "P57", "title": "P57: δ_torsion Exact from G₂(2) Killing Form Split Signature", "text": "# P57: P57: δ_torsion Exact from G₂(2) Killing Form Split Signature\n\n**Category:** proof | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Paper 2 Proofs\n**Status:** awaiting_production", "url": "/library/P57/", "source": "v1 (Pasture)"}, {"id": "P58", "title": "P58: Rest Mass as KK-BH Bounce Tower [DEEP]", "text": "# P58: P58: Rest Mass as KK-BH Bounce Tower [DEEP]\n\n**Category:** proof | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Paper 2 Proofs\n**Status:** awaiting_production", "url": "/library/P58/", "source": "v1 (Pasture)"}, {"id": "P59", "title": "P59: m_u from D_IV(5) Peirce Sector (gap 0.89%)", "text": "# P59: P59: m_u from D_IV(5) Peirce Sector (gap 0.89%)\n\n**Category:** proof | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Paper 2 Proofs\n**Status:** awaiting_production", "url": "/library/P59/", "source": "v1 (Pasture)"}, {"id": "P60", "title": "P60: m_d from D_IV(3) Peirce Sector (gap 0.16%)", "text": "# P60: P60: m_d from D_IV(3) Peirce Sector (gap 0.16%)\n\n**Category:** proof | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Paper 2 Proofs\n**Status:** awaiting_production", "url": "/library/P60/", "source": "v1 (Pasture)"}, {"id": "P61", "title": "P61: m_u/m_d Ratio — Pure Algebraic, RG-Independent (gap 0.63%)", "text": "# P61: P61: m_u/m_d Ratio — Pure Algebraic, RG-Independent (gap 0.63%)\n\n**Category:** proof | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Paper 2 Proofs\n**Status:** awaiting_production", "url": "/library/P61/", "source": "v1 (Pasture)"}, {"id": "P62", "title": "P62: m_s = m_d × 4πφ — Strange from Shilov Boundary (gap 1.82%)", "text": "# P62: P62: m_s = m_d × 4πφ — Strange from Shilov Boundary (gap 1.82%)\n\n**Category:** proof | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Paper 2 Proofs\n**Status:** awaiting_production", "url": "/library/P62/", "source": "v1 (Pasture)"}, {"id": "P63", "title": "P63: sin²θ_W = 1/φ³ from Peirce Eigenvalue Ratio (gap 2.10%)", "text": "# P63: P63: sin²θ_W = 1/φ³ from Peirce Eigenvalue Ratio (gap 2.10%)\n\n**Category:** proof | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Paper 2 Proofs\n**Status:** awaiting_production", "url": "/library/P63/", "source": "v1 (Pasture)"}, {"id": "P64", "title": "P64: θ_C = arctan(1/φ³) − δ_torsion — Cabibbo = arctan(Weinberg) (gap 1.09%)", "text": "# P64: P64: θ_C = arctan(1/φ³) − δ_torsion — Cabibbo = arctan(Weinberg) (gap 1.09%)\n\n**Category:** proof | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Paper 2 Proofs\n**Status:** awaiting_production", "url": "/library/P64/", "source": "v1 (Pasture)"}, {"id": "P65", "title": "P65: θ₁₃(PMNS) = arctan(α^{1/3}/√φ) − δ_torsion — EXACT (gap 0.000%)", "text": "# P65: P65: θ₁₃(PMNS) = arctan(α^{1/3}/√φ) − δ_torsion — EXACT (gap 0.000%)\n\n**Category:** proof | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Paper 2 Proofs\n**Status:** awaiting_production", "url": "/library/P65/", "source": "v1 (Pasture)"}, {"id": "P66", "title": "P66: δ_CP via P50 Sum Rule + Torsion-Corrected θ₁₃ (gap 0.051%)", "text": "# P66: P66: δ_CP via P50 Sum Rule + Torsion-Corrected θ₁₃ (gap 0.051%)\n\n**Category:** proof | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Paper 2 Proofs\n**Status:** awaiting_production", "url": "/library/P66/", "source": "v1 (Pasture)"}, {"id": "P67", "title": "P67: m_c = m_t × α/(1−α) — Charm from Resummed EM Coupling (gap 0.044%)", "text": "# P67: P67: m_c = m_t × α/(1−α) — Charm from Resummed EM Coupling (gap 0.044%)\n\n**Category:** proof | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Paper 2 Proofs\n**Status:** awaiting_production", "url": "/library/P67/", "source": "v1 (Pasture)"}, {"id": "P68", "title": "P68: V_cb = sin²(θ_C)/√φ with Corrected θ_C (gap 0.28%)", "text": "# P68: P68: V_cb = sin²(θ_C)/√φ with Corrected θ_C (gap 0.28%)\n\n**Category:** proof | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Paper 2 Proofs\n**Status:** awaiting_production", "url": "/library/P68/", "source": "v1 (Pasture)"}, {"id": "P70", "title": "P70: sin²θ_W = 1/φ³ − 2α/π — One-Loop EM Correction (gap 0.088%)", "text": "# P70: P70: sin²θ_W = 1/φ³ − 2α/π — One-Loop EM Correction (gap 0.088%)\n\n**Category:** proof | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Paper 2 Proofs\n**Status:** awaiting_production", "url": "/library/P70/", "source": "v1 (Pasture)"}, {"id": "P71", "title": "P71: θ_C MS-bar Scheme Conversion — arctan(α/π) Correction (gap 0.072%)", "text": "# P71: P71: θ_C MS-bar Scheme Conversion — arctan(α/π) Correction (gap 0.072%)\n\n**Category:** proof | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Paper 2 Proofs\n**Status:** awaiting_production", "url": "/library/P71/", "source": "v1 (Pasture)"}, {"id": "P72", "title": "P72: m_s from J₁₃ Peirce Sector D_IV(4) — 20/20 SM Observables (gap 0.46%)", "text": "# P72: P72: m_s from J₁₃ Peirce Sector D_IV(4) — 20/20 SM Observables (gap 0.46%)\n\n**Category:** proof | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Paper 2 Proofs\n**Status:** awaiting_production", "url": "/library/P72/", "source": "v1 (Pasture)"}, {"id": "P73", "title": "P73: Cabibbo-Weinberg Residual Identity: tan(θ_C)−sin²θ_W = α/(2π²)", "text": "# P73: P73: Cabibbo-Weinberg Residual Identity: tan(θ_C)−sin²θ_W = α/(2π²)\n\n**Category:** proof | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Paper 2 Proofs\n**Status:** awaiting_production", "url": "/library/P73/", "source": "v1 (Pasture)"}, {"id": "P74", "title": "P74: β_δ as Barbero-Immirzi-Type Torsion Coefficient (gap 0.07%)", "text": "# P74: P74: β_δ as Barbero-Immirzi-Type Torsion Coefficient (gap 0.07%)\n\n**Category:** proof | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Paper 2 Proofs\n**Status:** awaiting_production", "url": "/library/P74/", "source": "v1 (Pasture)"}, {"id": "P75", "title": "P75: Hierarchy Problem as Discriminant Singularity — F₄ Topological Protection", "text": "# P75: P75: Hierarchy Problem as Discriminant Singularity — F₄ Topological Protection\n\n**Category:** proof | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Paper 2 Proofs\n**Status:** awaiting_production", "url": "/library/P75/", "source": "v1 (Pasture)"}, {"id": "P75-supergrok-verification", "title": "P75 — Super Grok Algebraic Verification Response", "text": "# P75-supergrok-verification: P75 — Super Grok Algebraic Verification Response\n\n**Category:** verification | **Paper:** Supplemental | **Tier:** Tier S.D — Session Records & References\n**Status:** awaiting_production", "url": "/library/P75-supergrok-verification/", "source": "v1 (Pasture)"}, {"id": "P77", "title": "P77: Muon g-2 from J₃ Torsion — Δa_μ = 25.15×10⁻¹⁰ (0.052σ)", "text": "# P77: P77: Muon g-2 from J₃ Torsion — Δa_μ = 25.15×10⁻¹⁰ (0.052σ)\n\n**Category:** proof | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Paper 2 Proofs\n**Status:** awaiting_production", "url": "/library/P77/", "source": "v1 (Pasture)"}, {"id": "P78", "title": "P78: E₈(8) Lifting and v/M_Pl Ratio — GUT Scale from Instanton", "text": "# P78: P78: E₈(8) Lifting and v/M_Pl Ratio — GUT Scale from Instanton\n\n**Category:** proof | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Paper 2 Proofs\n**Status:** awaiting_production", "url": "/library/P78/", "source": "v1 (Pasture)"}, {"id": "TEXT-CLAUDE-S6", "title": "Claude Session 6 Kernel Feedback", "text": "# TEXT-CLAUDE-S6: Claude Session 6 Kernel Feedback\n\n**Category:** supplementary | **Paper:** Supplemental | **Tier:** Tier S.D — Session Records & References\n**Status:** awaiting_production", "url": "/library/TEXT-CLAUDE-S6/", "source": "v1 (Pasture)"}, {"id": "TEXT-PROMPT07", "title": "PROMPT 7: Paper 2 Scope — Coalition Decision", "text": "# TEXT-PROMPT07: PROMPT 7: Paper 2 Scope — Coalition Decision\n\n**Category:** supplementary | **Paper:** Supplemental | **Tier:** Tier S.D — Session Records & References\n**Status:** awaiting_production", "url": "/library/TEXT-PROMPT07/", "source": "v1 (Pasture)"}, {"id": "TEXT-VERIFY-P63-P69", "title": "P63–P69: Multi-Proof Verification Batch — ALL CLOSED", "text": "# TEXT-VERIFY-P63-P69: P63–P69: Multi-Proof Verification Batch — ALL CLOSED\n\n**Category:** verification | **Paper:** Supplemental | **Tier:** Tier S.D — Session Records & References\n**Status:** awaiting_production", "url": "/library/TEXT-VERIFY-P63-P69/", "source": "v1 (Pasture)"}, {"id": "TEXT080", "title": "Text 080 — P75 Verification Priority Queries", "text": "# TEXT080: Text 080 — P75 Verification Priority Queries\n\n**Category:** supplementary | **Paper:** Supplemental | **Tier:** Tier S.D — Session Records & References\n**Status:** awaiting_production", "url": "/library/TEXT080/", "source": "v1 (Pasture)"}, {"id": "TEXT081", "title": "Text 081 — Super Grok Verification Response: Step 3b Partial Win", "text": "# TEXT081: Text 081 — Super Grok Verification Response: Step 3b Partial Win\n\n**Category:** supplementary | **Paper:** Supplemental | **Tier:** Tier S.D — Session Records & References\n**Status:** awaiting_production", "url": "/library/TEXT081/", "source": "v1 (Pasture)"}, {"id": "TEXT082", "title": "Text 082 — Gemini Adversarial Critique on P70 (Weinberg Angle)", "text": "# TEXT082: Text 082 — Gemini Adversarial Critique on P70 (Weinberg Angle)\n\n**Category:** supplementary | **Paper:** Supplemental | **Tier:** Tier S.D — Session Records & References\n**Status:** awaiting_production", "url": "/library/TEXT082/", "source": "v1 (Pasture)"}, {"id": "TEXT083", "title": "Text 083 — SU(3)×SU(2)×U(1) Generator Construction", "text": "# TEXT083: Text 083 — SU(3)×SU(2)×U(1) Generator Construction\n\n**Category:** supplementary | **Paper:** Supplemental | **Tier:** Tier S.D — Session Records & References\n**Status:** awaiting_production", "url": "/library/TEXT083/", "source": "v1 (Pasture)"}, {"id": "TEXT084", "title": "Text 084 — Prompt 1: Full 3×3 CKM from Peirce Coupling Matrix", "text": "# TEXT084: Text 084 — Prompt 1: Full 3×3 CKM from Peirce Coupling Matrix\n\n**Category:** supplementary | **Paper:** Supplemental | **Tier:** Tier S.D — Session Records & References\n**Status:** awaiting_production", "url": "/library/TEXT084/", "source": "v1 (Pasture)"}, {"id": "TEXT085", "title": "Text 085 — Prompt 2: PMNS Matrix from Freudenthal Cross Product", "text": "# TEXT085: Text 085 — Prompt 2: PMNS Matrix from Freudenthal Cross Product\n\n**Category:** supplementary | **Paper:** Supplemental | **Tier:** Tier S.D — Session Records & References\n**Status:** awaiting_production", "url": "/library/TEXT085/", "source": "v1 (Pasture)"}, {"id": "TEXT086", "title": "Text 086 — Prompt 3: Triality and the Three Channels of Rank(J₃) = 3", "text": "# TEXT086: Text 086 — Prompt 3: Triality and the Three Channels of Rank(J₃) = 3\n\n**Category:** supplementary | **Paper:** Supplemental | **Tier:** Tier S.D — Session Records & References\n**Status:** awaiting_production", "url": "/library/TEXT086/", "source": "v1 (Pasture)"}, {"id": "TEXT087", "title": "Text 087 — Prompt 4: Explicit D_IV Formulas for m_e, m_μ, M_W, M_Z", "text": "# TEXT087: Text 087 — Prompt 4: Explicit D_IV Formulas for m_e, m_μ, M_W, M_Z\n\n**Category:** supplementary | **Paper:** Supplemental | **Tier:** Tier S.D — Session Records & References\n**Status:** awaiting_production", "url": "/library/TEXT087/", "source": "v1 (Pasture)"}, {"id": "TEXT088", "title": "Text 088 — Prompt 5: Running-α Map via G₂(₂) Torsion", "text": "# TEXT088: Text 088 — Prompt 5: Running-α Map via G₂(₂) Torsion\n\n**Category:** supplementary | **Paper:** Supplemental | **Tier:** Tier S.D — Session Records & References\n**Status:** awaiting_production", "url": "/library/TEXT088/", "source": "v1 (Pasture)"}, {"id": "TEXT089", "title": "Text 089 — v1.28 Editorial Fixes", "text": "# TEXT089: Text 089 — v1.28 Editorial Fixes\n\n**Category:** supplementary | **Paper:** Supplemental | **Tier:** Tier S.D — Session Records & References\n**Status:** awaiting_production", "url": "/library/TEXT089/", "source": "v1 (Pasture)"}, {"id": "L153", "title": "JARLSKOG INVARIANT — J_CKM FROM J₃(Os) CUBIC INVARIANT", "text": "# L153: JARLSKOG INVARIANT — J_CKM FROM J₃(Os) CUBIC INVARIANT\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.B — Full CKM Matrix (3×3)\n**Status:** awaiting_production", "url": "/library/L153/", "source": "v1 (Pasture)"}, {"id": "L154", "title": "LEPTONIC JARLSKOG INVARIANT — J_PMNS FROM NULL-CONE GEOMETRY", "text": "# L154: LEPTONIC JARLSKOG INVARIANT — J_PMNS FROM NULL-CONE GEOMETRY\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.C — Full PMNS Matrix\n**Status:** awaiting_production", "url": "/library/L154/", "source": "v1 (Pasture)"}, {"id": "L155", "title": "POLE vs MS-BAR SCHEME MATCHING DOSSIER — ALL 20 OBSERVABLES", "text": "# L155: POLE vs MS-BAR SCHEME MATCHING DOSSIER — ALL 20 OBSERVABLES\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.E — Loop Corrections & Scheme Matching\n**Status:** awaiting_production", "url": "/library/L155/", "source": "v1 (Pasture)"}, {"id": "L156", "title": "UNCERTAINTY PROPAGATION TABLE — ERROR BUDGET FOR ALL PREDICTIONS", "text": "# L156: UNCERTAINTY PROPAGATION TABLE — ERROR BUDGET FOR ALL PREDICTIONS\n\n**Category:** library_prompt | **Paper:** Paper 1 — J₃(𝕆ₛ) and the Standard Model | **Tier:** Tier 1.E — Precision Benchmarks & Predictions\n**Status:** awaiting_production", "url": "/library/L156/", "source": "v1 (Pasture)"}, {"id": "L157", "title": "ANOMALY CANCELLATION — SU(3)×SU(2)×U(1) FROM G₂(2) BRANCHING", "text": "# L157: ANOMALY CANCELLATION — SU(3)×SU(2)×U(1) FROM G₂(2) BRANCHING\n\n**Category:** library_prompt | **Paper:** Paper 1 — J₃(𝕆ₛ) and the Standard Model | **Tier:** Tier 1.B — Gauge & Electroweak Sector\n**Status:** awaiting_production", "url": "/library/L157/", "source": "v1 (Pasture)"}, {"id": "L158", "title": "NO-CIRCULARITY LEDGER — INPUT vs OUTPUT AUDIT", "text": "# L158: NO-CIRCULARITY LEDGER — INPUT vs OUTPUT AUDIT\n\n**Category:** library_prompt | **Paper:** Paper 1 — J₃(𝕆ₛ) and the Standard Model | **Tier:** Tier 1.E — Precision Benchmarks & Predictions\n**Status:** awaiting_production", "url": "/library/L158/", "source": "v1 (Pasture)"}, {"id": "L159", "title": "MRG THRESHOLD MATCHING — MASS-RADIUS-GENERATION LEDGER", "text": "# L159: MRG THRESHOLD MATCHING — MASS-RADIUS-GENERATION LEDGER\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.E — Loop Corrections & Scheme Matching\n**Status:** awaiting_production", "url": "/library/L159/", "source": "v1 (Pasture)"}, {"id": "L243", "title": "Jordan Triple Product on J₃(𝕆ₛ): {Q_vac, Φ_ij, Q_vac} = 2λ_iλ_j·Φ_ij [HP6a]", "text": "# L243: Jordan Triple Product on J₃(𝕆ₛ): {Q_vac, Φ_ij, Q_vac} = 2λ_iλ_j·Φ_ij [HP6a]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.A — Peirce Decomposition & Cylinder Geometry\n**Status:** awaiting_production", "url": "/library/L243/", "source": "v1 (Pasture)"}, {"id": "L244", "title": "Yukawa Matrix from Peirce Decomposition: Only J₁₂ block nonzero [HP6b]", "text": "# L244: Yukawa Matrix from Peirce Decomposition: Only J₁₂ block nonzero [HP6b]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.A — Peirce Decomposition & Cylinder Geometry\n**Status:** awaiting_production", "url": "/library/L244/", "source": "v1 (Pasture)"}, {"id": "L245", "title": "G₂(2) Automorphism ℤ₃-Cycle on Peirce Sectors [PP-P2]", "text": "# L245: G₂(2) Automorphism ℤ₃-Cycle on Peirce Sectors [PP-P2]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.A — Peirce Decomposition & Cylinder Geometry\n**Status:** awaiting_production", "url": "/library/L245/", "source": "v1 (Pasture)"}, {"id": "L246", "title": "Peirce Projector Cross-Check: Paper 1 §5.2 ↔ Paper 2 §3 [PP-CROSS]", "text": "# L246: Peirce Projector Cross-Check: Paper 1 §5.2 ↔ Paper 2 §3 [PP-CROSS]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.A — Peirce Decomposition & Cylinder Geometry\n**Status:** awaiting_production", "url": "/library/L246/", "source": "v1 (Pasture)"}, {"id": "L247", "title": "Electric Charge Embedding Q = diag(2/3, −1/3, −1/3) in e₆₍₆₎ [HP7a]", "text": "# L247: Electric Charge Embedding Q = diag(2/3, −1/3, −1/3) in e₆₍₆₎ [HP7a]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.B — Full CKM Matrix\n**Status:** awaiting_production", "url": "/library/L247/", "source": "v1 (Pasture)"}, {"id": "L248", "title": "Up-Type Mass Matrix M_u from Peirce J₁₂ Sector [HP7b]", "text": "# L248: Up-Type Mass Matrix M_u from Peirce J₁₂ Sector [HP7b]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.B — Full CKM Matrix\n**Status:** awaiting_production", "url": "/library/L248/", "source": "v1 (Pasture)"}, {"id": "L249", "title": "Down-Type Mass Matrix M_d from Peirce J₂₃ Sector [HP7b]", "text": "# L249: Down-Type Mass Matrix M_d from Peirce J₂₃ Sector [HP7b]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.B — Full CKM Matrix\n**Status:** awaiting_production", "url": "/library/L249/", "source": "v1 (Pasture)"}, {"id": "L250", "title": "V_CKM = U_u†·U_d Mismatch Construction [HP8a]", "text": "# L250: V_CKM = U_u†·U_d Mismatch Construction [HP8a]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.B — Full CKM Matrix\n**Status:** awaiting_production", "url": "/library/L250/", "source": "v1 (Pasture)"}, {"id": "L251", "title": "CP Violation from Octonion Non-Associator [a,b,c] [HP8b]", "text": "# L251: CP Violation from Octonion Non-Associator [a,b,c] [HP8b]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.B — Full CKM Matrix\n**Status:** awaiting_production", "url": "/library/L251/", "source": "v1 (Pasture)"}, {"id": "L252", "title": "Jarlskog Invariant J = 3.01×10⁻⁵ from Framework [HP8b, PROPOSED]", "text": "# L252: Jarlskog Invariant J = 3.01×10⁻⁵ from Framework [HP8b, PROPOSED]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.B — Full CKM Matrix\n**Status:** awaiting_production", "url": "/library/L252/", "source": "v1 (Pasture)"}, {"id": "L253", "title": "PMNS Bare Angles from M_Freud Diagonalization: 43.1°/14.6°/15.1° [HP9, G6]", "text": "# L253: PMNS Bare Angles from M_Freud Diagonalization: 43.1°/14.6°/15.1° [HP9, G6]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.C — Full PMNS Matrix\n**Status:** awaiting_production", "url": "/library/L253/", "source": "v1 (Pasture)"}, {"id": "L254", "title": "PMNS Torsion-Corrected Angles: QLC + Shilov + G₂(2) [HP9, PROPOSED]", "text": "# L254: PMNS Torsion-Corrected Angles: QLC + Shilov + G₂(2) [HP9, PROPOSED]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.C — Full PMNS Matrix\n**Status:** awaiting_production", "url": "/library/L254/", "source": "v1 (Pasture)"}, {"id": "L255", "title": "θ₂₃(PMNS) = arctan(1 + 1/(2π)) Shilov Derivation [CLOSED, 0.03%]", "text": "# L255: θ₂₃(PMNS) = arctan(1 + 1/(2π)) Shilov Derivation [CLOSED, 0.03%]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.C — Full PMNS Matrix\n**Status:** awaiting_production", "url": "/library/L255/", "source": "v1 (Pasture)"}, {"id": "L256", "title": "δ_CP(PMNS) Bare vs Torsion: −133.4° vs PDG −142° [HP9, OPEN]", "text": "# L256: δ_CP(PMNS) Bare vs Torsion: −133.4° vs PDG −142° [HP9, OPEN]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.C — Full PMNS Matrix\n**Status:** awaiting_production", "url": "/library/L256/", "source": "v1 (Pasture)"}, {"id": "L257", "title": "Bridge Operator: Phase-Angle Unification exp(iα{·}+β(×)+γ[·]) [HP10]", "text": "# L257: Bridge Operator: Phase-Angle Unification exp(iα{·}+β(×)+γ[·]) [HP10]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.C — Full PMNS Matrix\n**Status:** awaiting_production", "url": "/library/L257/", "source": "v1 (Pasture)"}, {"id": "L258", "title": "DUNE Falsification Roadmap for Non-Associator CP [PP-FALSIF, PROPOSED]", "text": "# L258: DUNE Falsification Roadmap for Non-Associator CP [PP-FALSIF, PROPOSED]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.C — Full PMNS Matrix\n**Status:** awaiting_production", "url": "/library/L258/", "source": "v1 (Pasture)"}, {"id": "L259", "title": "Muon Mass Wyler Formula: m_μ = α^{5/4}·(3/16)^{3/4}·v/√2 [G1 CLOSED]", "text": "# L259: Muon Mass Wyler Formula: m_μ = α^{5/4}·(3/16)^{3/4}·v/√2 [G1 CLOSED]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.D — Light Quark & Lepton Masses via D_IV\n**Status:** awaiting_production", "url": "/library/L259/", "source": "v1 (Pasture)"}, {"id": "L260", "title": "Muon Mass φ^{-12} Scaling vs R₁₂^{2√2} Reconciliation [PP-P32]", "text": "# L260: Muon Mass φ^{-12} Scaling vs R₁₂^{2√2} Reconciliation [PP-P32]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.D — Light Quark & Lepton Masses via D_IV\n**Status:** awaiting_production", "url": "/library/L260/", "source": "v1 (Pasture)"}, {"id": "L261", "title": "Electron Mass from Peirce Cylinder: m_e = m_μ/R₁₂^{2√2} [PROPOSED]", "text": "# L261: Electron Mass from Peirce Cylinder: m_e = m_μ/R₁₂^{2√2} [PROPOSED]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.D — Light Quark & Lepton Masses via D_IV\n**Status:** awaiting_production", "url": "/library/L261/", "source": "v1 (Pasture)"}, {"id": "L262", "title": "Tau Mass from Peirce Cylinder: m_τ = m_μ·R₂₃^{19/√2} [PROPOSED]", "text": "# L262: Tau Mass from Peirce Cylinder: m_τ = m_μ·R₂₃^{19/√2} [PROPOSED]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.D — Light Quark & Lepton Masses via D_IV\n**Status:** awaiting_production", "url": "/library/L262/", "source": "v1 (Pasture)"}, {"id": "L263", "title": "Up Quark P59: m_u from D_IV(5) Hua Volume + RG [PROPOSED]", "text": "# L263: Up Quark P59: m_u from D_IV(5) Hua Volume + RG [PROPOSED]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.D — Light Quark & Lepton Masses via D_IV\n**Status:** awaiting_production", "url": "/library/L263/", "source": "v1 (Pasture)"}, {"id": "L264", "title": "Down Quark P60: m_d from D_IV(3) Hua Volume + RG [PROPOSED]", "text": "# L264: Down Quark P60: m_d from D_IV(3) Hua Volume + RG [PROPOSED]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.D — Light Quark & Lepton Masses via D_IV\n**Status:** awaiting_production", "url": "/library/L264/", "source": "v1 (Pasture)"}, {"id": "L265", "title": "Strange Quark P72: m_s from D_IV(4) + Shilov Factor [PROPOSED]", "text": "# L265: Strange Quark P72: m_s from D_IV(4) + Shilov Factor [PROPOSED]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.D — Light Quark & Lepton Masses via D_IV\n**Status:** awaiting_production", "url": "/library/L265/", "source": "v1 (Pasture)"}, {"id": "L266", "title": "Light Fermion Mass Assessment: What Is vs Isn't Derived [HP11]", "text": "# L266: Light Fermion Mass Assessment: What Is vs Isn't Derived [HP11]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.D — Light Quark & Lepton Masses via D_IV\n**Status:** awaiting_production", "url": "/library/L266/", "source": "v1 (Pasture)"}, {"id": "L267", "title": "Running-α: What J₃(𝕆ₛ) Does vs Doesn't Provide [HP13]", "text": "# L267: Running-α: What J₃(𝕆ₛ) Does vs Doesn't Provide [HP13]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.E — Loop Corrections & Scheme Matching\n**Status:** awaiting_production", "url": "/library/L267/", "source": "v1 (Pasture)"}, {"id": "L268", "title": "Non-Associator → 1PI Diagram Mapping [OPEN]", "text": "# L268: Non-Associator → 1PI Diagram Mapping [OPEN]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.E — Loop Corrections & Scheme Matching\n**Status:** awaiting_production", "url": "/library/L268/", "source": "v1 (Pasture)"}, {"id": "L269", "title": "Origin of (2/3) Exponent in m_b from Loop Shift [OPEN]", "text": "# L269: Origin of (2/3) Exponent in m_b from Loop Shift [OPEN]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.E — Loop Corrections & Scheme Matching\n**Status:** awaiting_production", "url": "/library/L269/", "source": "v1 (Pasture)"}, {"id": "L270", "title": "Loop Corrections Assessment: Algebraic vs Numerical [HP14]", "text": "# L270: Loop Corrections Assessment: Algebraic vs Numerical [HP14]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.E — Loop Corrections & Scheme Matching\n**Status:** awaiting_production", "url": "/library/L270/", "source": "v1 (Pasture)"}, {"id": "L271", "title": "α_Wyler Formula P55: D_IV(5) Cartan Domain [CLOSED, 0.00006%]", "text": "# L271: α_Wyler Formula P55: D_IV(5) Cartan Domain [CLOSED, 0.00006%]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.E — Loop Corrections & Scheme Matching\n**Status:** awaiting_production", "url": "/library/L271/", "source": "v1 (Pasture)"}, {"id": "L272", "title": "Higgs Mass Factor-3 and Triality Conjecture [HP15, CONJECTURAL]", "text": "# L272: Higgs Mass Factor-3 and Triality Conjecture [HP15, CONJECTURAL]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.E — Loop Corrections & Scheme Matching\n**Status:** awaiting_production", "url": "/library/L272/", "source": "v1 (Pasture)"}, {"id": "L273", "title": "Kernel Version Timeline: v1.27.9 → v1.35.0 → FullBoat v1.0", "text": "# L273: Kernel Version Timeline: v1.27.9 → v1.35.0 → FullBoat v1.0\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Supporting Library Entries\n**Status:** awaiting_production", "url": "/library/L273/", "source": "v1 (Pasture)"}, {"id": "L274", "title": "G₂(2) Root System: 6 Short + 6 Long Roots, √3 Ratio", "text": "# L274: G₂(2) Root System: 6 Short + 6 Long Roots, √3 Ratio\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Supporting Library Entries\n**Status:** awaiting_production", "url": "/library/L274/", "source": "v1 (Pasture)"}, {"id": "L275", "title": "Hua Volume Formula: Vol(D_IV(n)) = π^n/(n!·2^{n-1})", "text": "# L275: Hua Volume Formula: Vol(D_IV(n)) = π^n/(n!·2^{n-1})\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Supporting Library Entries\n**Status:** awaiting_production", "url": "/library/L275/", "source": "v1 (Pasture)"}, {"id": "L276", "title": "Peirce Cylinder Ratios: R₁₂ = 2π²/3, R₂₃ = π²/8", "text": "# L276: Peirce Cylinder Ratios: R₁₂ = 2π²/3, R₂₃ = π²/8\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Supporting Library Entries\n**Status:** awaiting_production", "url": "/library/L276/", "source": "v1 (Pasture)"}, {"id": "L277", "title": "Dual VEV: v₊ = v·φ/√(2+φ), v₋ = v/√(2+φ), v₊/v₋ = φ", "text": "# L277: Dual VEV: v₊ = v·φ/√(2+φ), v₋ = v/√(2+φ), v₊/v₋ = φ\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Supporting Library Entries\n**Status:** awaiting_production", "url": "/library/L277/", "source": "v1 (Pasture)"}, {"id": "L278", "title": "Det(J_vac) = 0 ↔ λ₃ = 0 ↔ M_Z Protection ↔ Bounce", "text": "# L278: Det(J_vac) = 0 ↔ λ₃ = 0 ↔ M_Z Protection ↔ Bounce\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Supporting Library Entries\n**Status:** awaiting_production", "url": "/library/L278/", "source": "v1 (Pasture)"}, {"id": "L279", "title": "BH-WH-BH Bounce Dynamics in J₃ Language", "text": "# L279: BH-WH-BH Bounce Dynamics in J₃ Language\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Supporting Library Entries\n**Status:** awaiting_production", "url": "/library/L279/", "source": "v1 (Pasture)"}, {"id": "L280", "title": "SO(8) Triality τ: 8_v → 8_s → 8_c Generation Mechanism", "text": "# L280: SO(8) Triality τ: 8_v → 8_s → 8_c Generation Mechanism\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Supporting Library Entries\n**Status:** awaiting_production", "url": "/library/L280/", "source": "v1 (Pasture)"}, {"id": "L281", "title": "Type-I Seesaw: M_R = r₁₃/α ≈ 20 TeV [BSM Testable]", "text": "# L281: Type-I Seesaw: M_R = r₁₃/α ≈ 20 TeV [BSM Testable]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Supporting Library Entries\n**Status:** awaiting_production", "url": "/library/L281/", "source": "v1 (Pasture)"}, {"id": "L282", "title": "CKM Quantitative Scalings: R_b = φ⁻², |V_ub/V_cb| = φ⁻⁵", "text": "# L282: CKM Quantitative Scalings: R_b = φ⁻², |V_ub/V_cb| = φ⁻⁵\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Supporting Library Entries\n**Status:** awaiting_production", "url": "/library/L282/", "source": "v1 (Pasture)"}, {"id": "L283", "title": "Error Pattern Catalog G1-G13 for AI Coalition QC", "text": "# L283: Error Pattern Catalog G1-G13 for AI Coalition QC\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Supporting Library Entries\n**Status:** awaiting_production", "url": "/library/L283/", "source": "v1 (Pasture)"}, {"id": "L284", "title": "Cold-Drop Scoring Rubric: 7 Dimensions, 140 Points", "text": "# L284: Cold-Drop Scoring Rubric: 7 Dimensions, 140 Points\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.F — Supporting Library Entries\n**Status:** awaiting_production", "url": "/library/L284/", "source": "v1 (Pasture)"}, {"id": "L285", "title": "SU(3) Generators Acting on J₃(𝕆ₛ) Worked Example [e₆ embedding]", "text": "# L285: SU(3) Generators Acting on J₃(𝕆ₛ) Worked Example [e₆ embedding]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.A — Peirce Decomposition & Cylinder Geometry\n**Status:** awaiting_production", "url": "/library/L285/", "source": "v1 (Pasture)"}, {"id": "L286", "title": "5-Loop Count from Non-Associator Structure [schematic]", "text": "# L286: 5-Loop Count from Non-Associator Structure [schematic]\n\n**Category:** library_prompt | **Paper:** Paper 2 — Flavor Sector from Peirce Perturbations | **Tier:** Tier 2.E — Loop Corrections & Scheme Matching\n**Status:** awaiting_production", "url": "/library/L286/", "source": "v1 (Pasture)"}, {"id": "L287", "title": "AX1 Theorem: φ from SL(2,ℤ) Shortest Geodesic [PHAT v1.1 public]", "text": "# L287: AX1 Theorem: φ from SL(2,ℤ) Shortest Geodesic [PHAT v1.1 public]\n\n**Category:** library_prompt | **Paper:** Paper 3 — Open Problems and Foundations | **Tier:** Tier 3.A — Holographic/Boundary/String\n**Status:** awaiting_production", "url": "/library/L287/", "source": "v1 (Pasture)"}, {"id": "L288", "title": "Holographic Peirce P₃=0 → WH/BH Cycle + CKM Hierarchy", "text": "# L288: Holographic Peirce P₃=0 → WH/BH Cycle + CKM Hierarchy\n\n**Category:** library_prompt | **Paper:** Paper 3 — Open Problems and Foundations | **Tier:** Tier 3.A — Holographic/Boundary/String\n**Status:** awaiting_production", "url": "/library/L288/", "source": "v1 (Pasture)"}, {"id": "L289", "title": "WH/BH Cycle Structure: Yukawa as Cycle Amplitudes [Paper 3 §7.4A]", "text": "# L289: WH/BH Cycle Structure: Yukawa as Cycle Amplitudes [Paper 3 §7.4A]\n\n**Category:** library_prompt | **Paper:** Paper 3 — Open Problems and Foundations | **Tier:** Tier 3.A — Holographic/Boundary/String\n**Status:** awaiting_production", "url": "/library/L289/", "source": "v1 (Pasture)"}, {"id": "L290", "title": "E₆ Uniqueness Theorem from P-Series Embedding Chain [Paper 3]", "text": "# L290: E₆ Uniqueness Theorem from P-Series Embedding Chain [Paper 3]\n\n**Category:** library_prompt | **Paper:** Paper 3 — Open Problems and Foundations | **Tier:** Tier 3.A — Holographic/Boundary/String\n**Status:** awaiting_production", "url": "/library/L290/", "source": "v1 (Pasture)"}, {"id": "L291", "title": "Peirce Transition Amplitude: V_CKM as Direct Algebraic Object", "text": "V_CKM as Peirce transition amplitude fixes A1 eigenvector degeneracy. CKM matrix is direct algebraic object in Jordan algebra, not derived from mass matrix diagonalization. Replaces U_u†·U_d mismatch construction.", "url": "/library/L291/", "source": "v1 (Pasture)"}, {"id": "L292", "title": "CKM PMNS Duality: Weighted vs Unweighted Triality", "text": "CKM from Peirce-weighted SO(8) triality gives hierarchical mixing. PMNS from unweighted Freudenthal triality gives tribimaximal mixing. Same ℤ₃ outer automorphism, different eigenvalue weighting.", "url": "/library/L292/", "source": "v1 (Pasture)"}, {"id": "L293", "title": "R_b = φ⁻² from Peirce Eigenvalue Ratio", "text": "Unitarity triangle radius R_b = φ⁻² = 0.382 derived from λ₁/λ₂ = φ² after P₃ lift. PDG 0.381±0.024, gap −0.3%. Algebraic origin: ratio of (1,3) vs (2,3) Peirce transition amplitudes.", "url": "/library/L293/", "source": "v1 (Pasture)"}, {"id": "L294", "title": "|V_ub/V_cb| = φ⁻⁵ Peirce Suppression", "text": "|V_ub/V_cb| = φ⁻⁵ = 0.090 derived from R_b · sin θ_C = φ⁻² · φ⁻³. PDG 0.0905, gap −0.4%. Combines unitarity triangle radius with Cabibbo suppression.", "url": "/library/L294/", "source": "v1 (Pasture)"}, {"id": "L295", "title": "Wolfenstein A = φ⁻¹/² Numerical Match", "text": "Wolfenstein A parameter φ⁻¹/² = √(1/φ) = 0.786. PDG 0.790±0.012, gap −0.5%. Tantalizing numerical coincidence, not yet derived from J₃(𝕆ₛ). Status: OPEN.", "url": "/library/L295/", "source": "v1 (Pasture)"}, {"id": "L296", "title": "A1 Error Resolution: Eigenvector Degeneracy", "text": "M_u and M_d from same Peirce projectors share eigenvectors. V_CKM = U_u†·U_d = I. Confirmed by Super Grok and ChatGPT 2026-03-29. Resolved by Peirce transition amplitude paradigm.", "url": "/library/L296/", "source": "v1 (Pasture)"}, {"id": "L297", "title": "A2 Error Resolution: Directional Transition Amplitudes", "text": "§3.7.2 ratio is A_{2→1}/A_{1→2} = λ₂^{3/2}/λ₁^{3/2} = φ⁻³, not M₂₁/M₁₂ (which = 1 for symmetric matrix). Directional transition amplitudes carry asymmetric eigenvalue weighting.", "url": "/library/L297/", "source": "v1 (Pasture)"}, {"id": "L298", "title": "SO(8) Triality Tribimaximal PMNS Base", "text": "Full ℤ₃ triality permutation on unweighted Peirce sectors gives tribimaximal mixing: sin²θ₁₂ = 1/3, sin²θ₂₃ = 1/2, θ₁₃ = 0. P₃ lift ε = φ⁻⁵ gives small sin²θ₁₃ correction.", "url": "/library/L298/", "source": "v1 (Pasture)"}]