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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-f6768e9a9e8d9af5632fff03 · master f97433d9e6ce3586 · S339.

LIB2-250 · Withdrawn Schur-only proof of vanishing triplet masses

class RETIREDmath status (as printed) —attachment (as printed) —scorecard tier word (as printed) none printedhouse tier not yet assignedreview state PUBLISHEDentry version 7

Statement

The earlier proof sketch inferred vanishing triplet entries at every loop order from Schur block structure alone.

Scope

domain	The withdrawn zero-eigenvalue and all-orders inference, not the scalar-block structure or the separate numerical zero-mode result.

What this does not show. The withdrawn proof does not remove Schur block structure or independently overturn the reported numerical zeros.

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, Schur gauge-protection withdrawal — PDF p.151 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS

the previous version of this sketch concluded “zero entries for all triplet components at every loop order” from the block structure; that inference is withdrawn — Schur permits a nonzero scalar on each triplet block,

Appendix A, §A.7, Numerical zeros kept separate — PDF p.151 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → CONTEXT

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, Missing all-orders protection — PDF p.151 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → 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
registry	Rev32.1, A1538 F1; Appendix A p.146	—	shipped	The suite explicitly withdraws the Schur inference while retaining the reported A630 numerical zeros. This round performs neither the numerical test nor an all-orders argument.

What was said, and what retired it

historical statement	Schur block structure implies “zero entries for all triplet components at every loop order.”
where it stood	Earlier Appendix A proof sketch, quoted and withdrawn in Rev32.1; retained withdrawal at Rev32.7 p.146
retiring decision	A1538 F1, Rev32.1 Schur gauge-protection withdrawal; S290.4 falsifier-control note
what the suite prints now	the previous version of this sketch concluded “zero entries for all triplet components at every loop order” from the block structure; that inference is withdrawn — Schur permits a nonzero scalar on each triplet block, PDF p.146 (bytes of record)
successor records	LIB2-087 Schur block structure does not force a zero triplet eigenvalue
why retired	scientific_supersession + withdrawal — from the record's own words: `RESULT_CHANGED` → "falsifier"; `WITHDRAWN` → "withdrawal"

A successor is linked, never "derived from" the retired statement (charter §10.10).

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 (1)
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`	N/A	class RETIRED not governed by the source_labels rule
`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

Retirement companion to C2-114. The all-orders inference is distinct from the tree-level colour-isotropy subject C2-150; no identity between those claims is assumed.

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 249e831e3eccfdb901a251c4ad539e8ed57f7a78cf7f6d6ba444c4929862e9a8

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-250 | 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