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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-ccd2813c262256f788df0633 · master 3dbd976bd10bfb05 · S337.

LIB2-088 · Generic cross-block Yukawa loops are not yet covered by an Artin generator census

class CLAIMmath status (as printed) NOT_PRINTEDattachment (as printed) NOT_PRINTEDscorecard tier word (as printed) none printedhouse tier not yet assignedreview state PUBLISHEDentry version 9

Label sentence at the locator (PDF p.147 (bytes of record)):

Where a diagram’s internal algebra labels lie in a subalgebra generated by two elements, associativity follows by Artin;

Statement

Artin’s theorem establishes associativity when a diagram’s internal labels lie in a two-generated subalgebra; that containment is not established for generic cross-block Yukawa trilinears with three independent split-octonion entries.

Parts of the statement (2)

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 · Artin’s theorem establishes associativity when a diagram’s internal labels lie in a two-generated subalgebra (one claim)
p2 · that containment is not established for generic cross-block Yukawa trilinears with three independent split-octonion entries. (one claim)

Scope

carrier	Internal algebra labels in generic cross-block Yukawa diagrams
domain	The internal-label containment question; external momentum conservation does not settle it.
hypotheses	The ambient algebra is alternative.; Artin’s conclusion applies where the diagram’s labels lie in a subalgebra generated by two elements.
quantifier	The source-stated two-generator condition, not an unrestricted claim about all diagrams.
real form	Split octonions Os

What this does not show. Lack of established two-generator containment is not a proof that a particular loop correction is non-associative or nonzero.

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.7.8(ii), Conditional Artin application — PDF p.153 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS

Where a diagram’s internal algebra labels lie in a subalgebra generated by two elements, associativity follows by Artin;

Appendix A, §A.7.8(ii), Unestablished trilinear containment — PDF p.153 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS

for the generic cross-block Yukawa trilinear (three independent split-octonion entries, Paper 6) that containment is not established — momentum conservation constrains momenta, not the number of independent internal octonionic directions

Appendix A, §A.7.8(ii), Outstanding object — PDF p.153 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → CONTEXT · the lanes disagreed; resolved by PI ruling R89 as CONTEXT — a ruling whose gloss the house owes; a use resolved by ruling never anchors PUBLISHED

A diagram-by-diagram generator census is the named outstanding object.

Evidence (availability is not outcome)

kind	reference	line / key	availability	note
registry	Rev32.1 scope correction, A1538 F5; Appendix A §A.7.8(ii), p.147	—	shipped	The supplied source limits Artin protection and names the missing census; no diagrammatic calculation is performed here.

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-F05b` A1647	PROPAGATION	CONFIRMED	The conditional Artin predicate is not propagated: the same passage says 4-point functions are "the first place" three independent octonionic directions meet and that G₂ gives "a consistent associative envelope for all leading-order perturbation theory", both of which need the outstanding generator census.	appendix_a_lagrangian_derivation.tex:665–679. paper: REV33.2_PENDING S329·A1647 item 6	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
candidate ids (frozen list S304)	C2-114

Drafting-lane note

Artin-scope child of C2-114. This is a limit on the argument, not a new loop result. The two-point and generic three-entry statements are not conflated through momentum conservation.

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 548f99fae7157b44f8e55dd8d9d8a9dc7f83bc9e6d227d44f0f7fdc21c310116

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-088 | 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