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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-597fa49a7de2302f48a26dee · master c7e92a7e45eaadf0 · S342.

LIB2-175 · The supported MOS quotient has rank three and relative rank two

class CLAIMmath status (as printed) NOT_PRINTEDattachment (as printed) NOT_PRINTEDscorecard tier word (as printed) none printedhouse tier not yet assignedreview state PUBLISHEDentry version 12

Label sentence at the locator (PDF p.310 (bytes of record)):

ΠMOS has rank 3 and relative rank 2 < 5, hence

Statement

The supported observation quotient ΠMOS has rank 3 and relative rank 2 < 5; it is not the full microscopic loading.

Parts of the statement (4)

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 · The supported observation quotient ΠMOS has rank 3 and relative rank 2 < 5 (cut further below)
p1-p1 · The supported observation quotient ΠMOS has rank 3 (one claim)
p1-p2 · relative rank 2 < 5 (one claim)
p2 · it is not the full microscopic loading. (one claim)

Scope

carrier	The supported MOS observation quotient from paired and annular carriers
domain	The finite supported quotient, not the microscopic support-restoring map.
hypotheses	Use the registered pair coisometry, Hodge frame and annular Fourier support.
quantifier	The registered construction and its stated premises.

What this does not show. The finite quotient does not restore missing microscopic modes or discharge the full observation-map 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, §11, Theorem 11.2: partial isometry — PDF p.328 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: grok read OUR_QUOTE_AS_PRINTED → CONTEXT · gemini read OUR_QUOTE_AS_PRINTED → CONTEXT · gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → CONTEXT

exact partial isometry (Π̃Π̃T = Pann , Π̃T Π̃ = PV4 ) killing all pair-difference modes;

The text extraction above lost mathematical typography. Restored from the sealed TeX source (rev32.7/tex/appendix_t_cartan_observation.tex:730-732): exact partial isometry (Π̃Π̃ᵀ=Pₐₙₙ, Π̃ᵀΠ̃=P_(V₄)) killing all pair-difference modes; (R87 house restoration: rendered from the tex, not the quote; the quote above is what the machine gate matched)

Appendix T, §11, Binding rank fence — PDF p.328 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read OUR_QUOTE_AS_PRINTED → SUPPORTS · gemini read OUR_QUOTE_AS_PRINTED → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS

ΠMOS has rank 3 and relative rank 2 < 5, hence

Appendix T, §11, Microscopic loading remains unconstructed — PDF p.328 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read OUR_QUOTE_AS_PRINTED → SUPPORTS · gemini read OUR_QUOTE_AS_PRINTED → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS · grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS

this is the observable quotient of a still unconstructed microscopic loading.

Evidence (availability is not outcome)

kind	reference	line / key	availability	note
computational	A1448; Appendix T §11, Theorem 11.2 and rank fence, p.310	—	unknown	The source reports exact support and rank checks. The quotient matrices and original outputs 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
`3`	PDF p.310 (bytes of record)	suite text p.310 only (no kernel line found): binding ΠMOS rank fence
`2`	PDF p.310 (bytes of record)	suite text p.310 only (no kernel line found): binding ΠMOS rank fence
`5`	PDF p.310 (bytes of record)	suite text p.310 only (no kernel line found): binding ΠMOS rank fence

Typed links

type	target	licensed by
`related_to` (never evidential)	LIB2-174 The record-quotient observation composite is unique under its seven premises	—

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

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-MOSQ-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	A1448 s927
candidate ids (frozen list S304)	C2-092

Drafting-lane note

C2-092 retains the supported-quotient object. The later rank-two support certificate is a separate statement, not another name for this quotient. No full-rank transfer is inferred.

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 add96a1abbf9ad86a08030c878f8f28cd98e63ae1f3d007652bfead8b9048c46

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-175 | 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