PUBLISHED under R67 (condition T-B) — NOT house-adjudicated. Build S371a. What PUBLISHED means here (R72): two non-drafting AI lanes (gemini + grok) read this record's anchor citation on different objects and agreed it SUPPORTS the record's statement; no citation on the record is disputed as support; its machine certificate is current. What it does not mean: no person has signed off on this record (adjudication: NOT_ADJUDICATED), the drafting lane's own reads count for nothing, and 3 of 3 unblocked uses were REVIEWED — the rest were read by one lane or none. Every label shown is the label as printed in the suite of record (Rev33.1_S369 (PDF sha256 b64ddcd9e16a6dcd…)); no house tier is assigned. The state is recomputed from the uses on every build and is withdrawn if they stop justifying it. Receipt: condition R67-TB · anchor SU-5e70c799781d34648e8d7258 · master 7147ae21feb6c82a · S338.

LIB2-171 · The pure MacDowell–Mansouri quadratic form is not a positive covariance

class CLAIMmath status (as printed) NOT_PRINTEDattachment (as printed) NOT_PRINTEDscorecard tier word (as printed) none printedhouse tier not yet assignedreview state PUBLISHEDentry version 7

Label sentence at the locator (PDF p.305 (bytes of record)):

On the 16-representation, BC = −tr(TI TJ ) = 4I10 exactly, inertia (10, 0); BMM = tr(ΓTI TJ ) has characteristic polynomial

Statement

On the registered 16-representation, BMM = tr(ΓTI TJ) has inertia (3,3,4), so the pure MM/EH weight cannot be a positive coercive covariance.

Scope

carrier	The MacDowell–Mansouri quadratic form on the registered generator space
domain	The pure MM/EH quadratic form, distinct from the positive completion cone.
hypotheses	Use the registered 16-representation, generators and chirality trace.
quantifier	The registered construction and its stated premises.

What this does not show. This finite-algebraic obstruction does not exclude the positive completion family or prove that a finite Cartan state is Einstein gravity.

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.

Sources in the suite of record

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, Theorem 7.3: representation and quadratic form — PDF p.322 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS

On the 16-representation, BC = −tr(TI TJ ) = 4I10 exactly, inertia (10, 0); BMM = tr(ΓTI TJ ) has characteristic polynomial

Appendix T, §7, Theorem 7.3: inertia — PDF p.322 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS

λ4 (λ − 4)3 (λ + 4)3 , hence inertia (3, 3, 4) — self-dual positive, anti-self-dual negative, transvections null.

The text extraction above lost mathematical typography. Restored from the sealed TeX source (rev32.7/tex/appendix_t_cartan_observation.tex:389-390): λ⁴(λ-4)³(λ+4)³, hence inertia (3,3,4) — self-dual positive, anti-self-dual negative, transvections null. (R87 house restoration: rendered from the tex, not the quote; the quote above is what the machine gate matched)

Appendix T, §7, Covariance obstruction — PDF p.322 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS

The pure MM/EH weight cannot be a positive coercive covariance.

Evidence (availability is not outcome)

kind	reference	line / key	availability	note
computational	s920-W1/W2; A1442, Appendix T §7, p.305	—	unknown	The source reports the exact quadratic forms and characteristic polynomial; no inertia calculation or kernel is run here.

The numbers this record declares, and where each one's digits come from

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
`16`	PDF p.305 (bytes of record)	suite text p.305: representation and BMM inertia in Theorem 7.3; no kernel line found
`3`	PDF p.305 (bytes of record)	suite text p.305: representation and BMM inertia in Theorem 7.3; no kernel line found
`4`	PDF p.305 (bytes of record)	suite text p.305: representation and BMM inertia in Theorem 7.3; no kernel line found

Typed links

type	target	licensed by
`related_to` (never evidential)	LIB2-169 The Euclidean MM/EH action has the stated conformal instability	—
`related_to` (never evidential)	LIB2-170 A reflection-positive Cartan state exists at finite regulator	—

Why this record is PUBLISHED (R67, condition T-B)

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 (3)
a SUPPORTS use on the predicate is DISPUTED	no
machine certificate current	yes

Machine certificate (R68)

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

check	result	reason
`schema_valid`	PASS	exercised
`basis_current`	PASS	exercised
`quote_located`	PASS	exercised
`labels_literal`	PASS	exercised
`edges_resolved`	PASS	exercised
`bindings_valid`	PASS	exercised

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.

History

March library (v1) antecedents	no legacy antecedent identified
Track-2 claim ids	F-SIGN-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)	C2-095

Drafting-lane note

C2-095 keeps the explicit inertia and pure-weight qualifier. The form is not the positive Killing-type covariance BC. No unprinted real-form classification or continuum conclusion is added.

Receipt

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 2313fcbd2ca764d9b3189c4415bac3c4a55b69620258cc98289d42853b6070f3

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-171 | 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