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 2 of 2 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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-733817f1137df1af9ecfd4d9 · master bd2d1a4de7da2b44 · S338.

LIB2-185 · The rank-two support certificate excludes a rank-five extension at the MOS tier

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.316 (bytes of record)):

A rank-5 extension exists as ambient linear algebra, but the record-support condition forbids it at the printed MOS tier by an exact rank-two support certificate [A1560].

Statement

An ambient rank-5 extension exists, but the record-support condition excludes it at the printed MOS tier by an exact rank-two support certificate.

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 · An ambient rank-5 extension exists (one claim)
p2 · but the record-support condition excludes it at the printed MOS tier by an exact rank-two support certificate. (one claim)

Scope

carrier	The record-support constraint and an ambient linear-algebra extension
domain	The tier-local support obstruction, not nonexistence of the ambient extension.
hypotheses	Retain the record-support condition of the printed MOS quotient tier.
quantifier	The registered construction and its stated premises.

What this does not show. The support certificate does not exclude a microscopic map outside the printed quotient tier or deny the ambient rank-five construction.

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, §15.3, Ambient extension and tier-local obstruction — PDF p.334 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS

A rank-5 extension exists as ambient linear algebra, but the record-support condition forbids it at the printed MOS tier by an exact rank-two support certificate [A1560].

Appendix T, §15.3, Required microscopic reopening — PDF p.334 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → CONTEXT

reopening it requires a genuinely microscopic support-restoring operator-system map.

Evidence (availability is not outcome)

kind	reference	line / key	availability	note
computational	A1560; Appendix T §15.3, p.316	—	unknown	The source reports the exact support certificate; its matrices and original checker are not supplied.

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
`5`	PDF p.316 (bytes of record)	suite text p.316 only (no kernel line found): rank-5 ambient extension and rank-two support certificate
`2`	PDF p.316 (bytes of record)	suite text p.316 only (no kernel line found): rank-two support certificate

Typed links

type	target	licensed by
`related_to` (never evidential)	LIB2-175 The supported MOS quotient has rank three and relative rank two	—
`related_to` (never evidential)	LIB2-184 The registered normalization census contains no forcing row	—

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

states a predicate	yes
uses on the record · unblocked	2 · 2
uses any lane has read	2 of 2
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`	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-NORM-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	A1560
candidate ids (frozen list S304)	C2-135

Drafting-lane note

Support child of C2-135. The rank-two certificate is not identified with the rank-three observable quotient G-179. Availability of the source statement is not availability of its certificate payload.

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 a753bba79e682b499380b8ab998465a50b357e5d1efcc911197d6d7723d0379c

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-185 | 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