Claims & Evidence Registrar › H05
Label sentence at the locator (PDF p.277 (bytes of record)):
No positive equivariant polarization exists in the split-G2 family.
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.
Each part is a clause of the statement above, cut so that one part makes one claim. A reader naming the clause a quote supports can name the part.
| carrier | Equivariant polarizing involutions on the split-octonion carrier |
|---|---|
| domain | The enumerated equivariant involution family, not arbitrary polarizations or other real forms. |
| group | Der(Os)-equivariance |
| hypotheses | The commutant of Der(Os) in End(Os) has the source-reported dimension two.; The split norm on Im Os has signature (3,4).; Use involutions of the stated form J = sP1 + tPIm; Appendix Q retains its κphys conditional tier. |
| quantifier | The declared source class only. |
| real form | Split G2 / split octonions |
Scientific status: UNDER REVIEW — the house has not adjudicated CURRENT / CONTESTED for this record (charter §10.3); a drafted claim is a claim under review, not a result.
Key — use ≠ record. A review state printed on a source use below names that use — one citation of the suite, read by the lane named in its warrant — not this record. The record's own review state is the one in the table above and is unchanged by any use-level state; a use may be LANE_PROPOSED or REVIEWED while the record it sits on remains IN_REVIEW (R45, R49).
Quotes are verbatim from the sha-pinned text extraction of the Rev33.1 PDF (A1584 §2.2, S309): mathematical typography — radicals, exponents, ≅ — can appear displaced in the extracted line. The PDF page is authoritative; the quote is what the machine gate matched.
Appendix Q, §3(ii), Polarization obstruction — PDF p.292 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS
No positive equivariant polarization exists in the split-G2 family.
Appendix Q, §3(ii), Enumerated involution signatures — PDF p.292 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS
all four equivariant involutions of the form J = s P1 + t PIm give sig(G·J) ∈ {(4, 4), (5, 3), (3, 5), (4, 4)} — none positive.
Appendix Q, §3, Real-form premise — PDF p.292 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → CONTEXT · grok read OUR_QUOTE_AS_PRINTED → CONTEXT · gemini read OUR_QUOTE_AS_PRINTED → CONTEXT
Both results are computed in the split real form and inherit the real-form declaration of Appendix X: signatures in this family are a consequence of a declared input, not an intrinsic feature, and must be quoted with that premise named.
| kind | reference | line / key | availability | note |
|---|---|---|---|---|
| registry | A1481; Appendix Q §3(ii), p.277 | — | shipped | The suite reports the commutant and four involution signatures; no new commutant or inertia calculation is run here. |
This table covers the values this record DECLARES, not every numeral printed on this page: group labels such as E7(7), section numbers and page numbers are not declared values and are not listed here.
| value as printed | page | digit source |
|---|---|---|
2 | PDF p.277 (bytes of record) | suite text p.277 only (no kernel line found) |
1 | PDF p.277 (bytes of record) | suite text p.277 only (no kernel line found) |
4 | PDF p.277 (bytes of record) | suite text p.277 only (no kernel line found) |
5 | PDF p.277 (bytes of record) | suite text p.277 only (no kernel line found) |
3 | PDF p.277 (bytes of record) | suite text p.277 only (no kernel line found) |
Each row is a house-declared use of a registered premise (R37). DECLARED is the house's editorial judgment only; a use becomes REVIEWED when two non-drafting lanes, reading different objects, agree the premise is LOAD_BEARING for this record's result. REJECTED rows were retired by ruling and are shown for provenance.
| use | state | premise | role | why the house declared it · reads |
|---|---|---|---|---|
USE-0040 | REVIEWED by lanes (R49c) | PRM-002 (PRM-002/r1) — Split Jordan carrier | hypothetical_assumption | R98 (PI, S334), completing R95. Use SU-6c9c1541b6a7d62c34b89813 quotes "computed in the split real form and inherit the real-form declaration of Appendix X: signatures in this family are a consequence of a declared input, not an intrinsic feature". BOTH LANES returned NEITHER (D1309/D1310) and were right: not evidence for the predicate, but the premise it rests on. PRM-002 states J3(Os) has signature (15,12), indefinite and not formally real — the declaration those signatures inherit. PRM-011 (compact colour real form, alpha, Appendix N) REJECTED: different object; LIB2-108 rests on it. NOT VERIFIED, recorded not asserted: (1) that PRM-002's page is literally Appendix X — no appendix header on it, so this rests on a subject-matter match, not a located passage; (2) PRM-002 is DRAFTED and had no record resting on it — this is its first edge.
|
| type | target | licensed by |
|---|---|---|
related_to (never evidential) | LIB2-104 The bare quartic is not stationary at the registered golden boundary point | — |
related_to (never evidential) | LIB2-096 The available compact part is too small for compact colour | — |
rests_on_premise | PRM-002 Split Jordan carrier J3(O_s) (indefinite trace form) | rev32.7/tex/appendix_q_golden_vacuum_spectrum.tex:93-96 (QUOTE_TEX_ANCHORS_S329, class UNIQUE, pdf p.277, quote_sha16 7b7b4af206d6bc12) |
| states a predicate | yes |
|---|---|
| uses on the record · unblocked | 3 · 3 |
| uses any lane has read | 3 of 3 |
| REVIEWED SUPPORTS use on the predicate, read by two non-drafting lanes | yes (2) |
| a SUPPORTS use on the predicate is DISPUTED | no |
| machine certificate current | yes |
| state | MACHINE_CHECKS_PASSED | |||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| policy | sgtoe-clearance-policy-1.0-RATIFIED · sha16 ef7d6e7690514311 | |||||||||||||||||||||
| bound to master | aad7a3ec6ce3b510 (the master the checks ran on; issued 2026-09-26T05:06Z) | |||||||||||||||||||||
| checks |
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A certificate says the record is well-formed, current, quote-on-page, label-literal, edge-resolved and binding-consistent on the bytes it was issued on. It is not a review, and it goes STALE the moment the master moves under it (R68). It is one conjunct of the PUBLISHED condition (R67), never the whole of it.
| March library (v1) antecedents | no legacy antecedent identified |
|---|---|
| serials | A1481 |
| candidate ids (frozen list S304) | C2-042 |
Source-backed missing proposal T4-17, associated with C2-042. The signature list is retained as printed, including its repeated value; no unprinted positive form or compactification is substituted.
round D1253 · parsed 2026-09-06T00:06Z · machine gates passed: CONTRACT, G1-quote-on-page, G2-numerals-declared, G4-ids-resolve, DAG-acyclic · content sha256 d9ecd47fc9bbcf6b5b912df6090000a2edbb2ec04650549f2c1e0e1e0a7cec52
Reviewer verdict line (one per entry, as text): LIB2-105 | PASS or FAIL(G1–G8) or NOT RUN | quote | PDF page | one sentence. G1 source supports the exact scoped assertion · G2 evidence class fits (numbers ≡ digit source) · G3 labels as printed, not converted · G4 comparison typed · G6 public scope · G7 history real · G8 caution present and true. Machine surfaces: index.json · capsule.md.
Generated from library_v2.jsonl. Declared volatile fields (R36): BUILD_STAMP.
BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02