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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-9d596c7c93c78b68fb6f6541 · master 6d82da907c52e8e6 · S329.

LIB2-087 · Schur block structure does not force a zero triplet eigenvalue

class CLAIMmath status (as printed) NOT_PRINTEDattachment (as printed) NOT_PRINTEDscorecard tier word (as printed) none printedhouse tier not yet assignedreview state PUBLISHEDentry version 8

Label sentence at the locator (PDF p.146 (bytes of record)):

Schur’s lemma ensures the block structure at the algebraic representation level — no singlet–triplet mixing, and scalar action λI on each irreducible triplet block; it does not by itself force λ = 0

Statement

Schur symmetry supplies singlet–triplet block separation and scalar action λI on each irreducible triplet block, but does not force λ = 0.

Parts of the statement (3)

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.

p1 · Schur symmetry supplies singlet–triplet block separation (one claim)
p2 · scalar action λI on each irreducible triplet block (one claim)
p3 · but does not force λ = 0. (one claim)

Scope

carrier	The representation-level Coleman–Weinberg Hessian at the registered vacuum
domain	The distinction between a permitted scalar block and a numerically vanishing eigenvalue.
group	The source’s G2 representation decomposition
hypotheses	Use the invariant block decomposition described in Appendix A §A.7.5.
quantifier	What follows from the stated representation symmetry alone.

What this does not show. This correction neither reproduces the separate numerical zeros nor provides an all-orders protection theorem.

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 A, §A.7.5, Rev32.1 Schur correction — PDF p.151 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS

Schur’s lemma ensures the block structure at the algebraic representation level — no singlet–triplet mixing, and scalar action λI on each irreducible triplet block; it does not by itself force λ = 0

Appendix A, §A.7.5, Numerical zeros have separate provenance — PDF p.151 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → CONTEXT · the lanes disagreed; resolved by PI ruling R89 as SUPPORTS — a ruling whose gloss the house owes; a use resolved by ruling never anchors PUBLISHED

The six triplet zeros stand as the certified numerical result of [A630], not as a consequence of this representation-theoretic argument.

Appendix A, §A.7.5, All-orders argument not supplied — PDF p.151 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: grok read THE_RECORD → CONTEXT · gemini read SUITE_TEXT_EXTRACT → CONTEXT

An all-orders statement would require a separate shift symmetry, Ward identity, BRST, or non-renormalisation argument and is not provided here.

Evidence (availability is not outcome)

kind	reference	line / key	availability	note
analytic	Appendix A §A.7.5, corrected representation-level argument, p.146	—	shipped	The source explicitly separates the Schur consequence from A630’s numerical result; no numerical zero is reverified.

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
`0`	PDF p.146 (bytes of record)	closed form: scalar action λI does not force λ = 0, printed in §A.7.5

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 (2)
a SUPPORTS use on the predicate is DISPUTED	no
machine certificate current	yes

Referee findings (R73)

Raised by a lane acting as referee and re-measured by the house before being listed (a lane's word alone is not a finding). Only a CONFIRMED finding against the record's predicate blocks PUBLISHED; the others are printed so a reader sees them.

finding	scope	state	what	evidence	affects this record's predicate?
`A1647-F05a` A1647	PROPAGATION	CONFIRMED	The corrected predicate (Schur does not force λ = 0) is not propagated: §A.7.6 still says "the G₂ branching forces the spectrum {+32, 0⁶, −32}" while attributing the zeros to A630.	appendix_a_lagrangian_derivation.tex:581–589. paper: REV33.2_PENDING S329·A1647 item 5	no — the predicate is unaffected

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	A-COLD-SCOPE-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	A1538 A630
candidate ids (frozen list S304)	C2-114

Drafting-lane note

Schur-scope child of C2-114. The imported Historical label belongs to its source record; this current entry preserves the corrected implication. The withdrawn zero-eigenvalue inference is not reinstated.

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 bae9a64d75a3e506d792063cb269fbcc83de16a2005980ea8284e03ca9fde6fb

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-087 | 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