Claims & Evidence Registrar › H07
Label sentence at the locator (PDF p.305 (bytes of record)):
the quaternion commutant units commute with Dfree , and det(mI + D) = m8 (m2 + 3)8 exactly. Kramers positivity is confirmed.
On the registered orthonormalized branch module, det(mI + D) = m⁸(m² + 3)⁸ gives the source's free quaternionic fermion positivity.
| carrier | The free quaternionic fermion operator on the h-orthonormalized branch module |
|---|---|
| domain | The specified free fermion measure, not a generic interacting chiral measure. |
| hypotheses | Use the source's real symmetric Euclidean gammas and quaternionic commutant commuting with Dfree. |
| quantifier | The registered construction and its stated premises. |
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 T, §7, Proposition 7.5: free determinant — PDF p.322 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS · grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS
the quaternion commutant units commute with Dfree , and det(mI + D) = m8 (m2 + 3)8 exactly
Appendix T, §7, Proposition 7.5: non-generic positivity — PDF p.322 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → CONTEXT
Fence: positivity is not generic (break controls in both lanes); the free sector is closed, the interacting chiral sector is open.
Appendix T, §7, Proposition 7.5: determinant-line requirement — PDF p.322 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → CONTEXT
a gauge-invariant, reflection-compatible, globally phase-consistent trivialization of the chiral determinant line — anomaly cancellation is necessary but not sufficient.
| kind | reference | line / key | availability | note |
|---|---|---|---|---|
| computational | s920-W6; Appendix T §7, Proposition 7.5, p.305 | — | unknown | The suite reports the determinant and positivity controls; the free operator matrices, checker and outputs are not supplied. |
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 |
|---|---|---|
8 | PDF p.305 (bytes of record) | closed form: det(mI + D) = m8(m2 + 3)8 printed in Proposition 7.5 |
2 | PDF p.305 (bytes of record) | closed form: det(mI + D) = m8(m2 + 3)8 printed in Proposition 7.5 |
3 | PDF p.305 (bytes of record) | closed form: det(mI + D) = m8(m2 + 3)8 printed in Proposition 7.5 |
| type | target | licensed by |
|---|---|---|
related_to (never evidential) | LIB2-170 A reflection-positive Cartan state exists at finite regulator | — |
related_to (never evidential) | LIB2-109 The loaded one-generation dictionary cancels the stated anomalies | — |
| 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 (1) |
| 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 |
|---|---|
| Track-2 claim ids | F-RP-01 — cross-reference; the Track 1 / Track 2 join sets each one against what the sealed suite prints for this record. Where they differ, the suite is the record. |
| serials | A1442 s920 |
| candidate ids (frozen list S304) | C2-094 |
Source-printed free-fermion companion to C2-094 and positive precursor of T4-19. The interacting determinant-line problem remains separate; no anomaly-to-positivity implication is added.
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 d13c8c543c29af8291571463b64b83525c22e1f4c82d9b0f78f57e9475f004eb
Reviewer verdict line (one per entry, as text): LIB2-188 | 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