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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-1a9ce2d281e9065fe180814b · master ac37c14788254b3d · S327.

LIB2-048 · The selected Jordan vacuum pair has Gram determinant seven

class CLAIMmath status (as printed) NOT_PRINTEDattachment (as printed) NOT_PRINTEDscorecard tier word (as printed) none printedhouse tier not yet assignedreview state PUBLISHEDentry version 7

Label sentence at the locator (PDF p.153 (bytes of record)):

The Jordan pair (Jvac , Jvac # ) has Gram determinant 7, fixing the mismatch geometry and the normalization of the (1, 3) sector.

Statement

For the selected Jordan pair (Jvac,Jvac#), the trace-form Gram determinant is 7.

Scope

carrier	The Jordan vacuum and adjoint pair
domain	Internal Gram evaluation.
hypotheses	Use the selected golden vacuum, its Jordan adjoint and the registered trace form.
quantifier	The registered construction only.
real form	J3(Os)

What this does not show. The Gram value does not derive the physical atmospheric registration and is distinct from imposing DET-7 as a selector premise.

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 B, §B.5, Structural support (a): DET-7 — PDF p.159 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS

The Jordan pair (Jvac , Jvac # ) has Gram determinant 7, fixing the mismatch geometry and the normalization of the (1, 3) sector.

Paper 3, §5.4, Internal identity and physical-registration boundary — PDF p.64 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → CONTEXT

The current physical θ23 row is therefore Loaded-correspondence; the number and the internal theorem do not move.

Evidence (availability is not outcome)

kind	reference	line / key	availability	note
analytic	Paper 3, Theorem 3.2, p.50; Appendix B §B.5, p.153	—	shipped	The suite states the Gram evaluation; this record does not independently recalculate it.

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
`7`	PDF p.153 (bytes of record)	closed form: the Jordan pair's Gram determinant 7 is printed in DET-7 structural support

Typed links

type	target	licensed by
`related_to` (never evidential)	LIB2-046 The golden spectrum obeys the reciprocal-square identity	—
`related_to` (never evidential)	LIB2-047 The working golden vacuum has unit Jordan determinant	—
`related_to` (never evidential)	LIB2-018 DET-7 is a structural postulate in the algebraic selector	—
`cited_by_section`	E-C05.1.claims-used (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0161
`cited_by_section`	E-C05.1.prior-art (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0178

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
candidate ids (frozen list S304)	C2-003

Drafting-lane note

This is the evaluated-invariant face of C2-003; G-022 records its distinct premise role. G-001 remains the internal mismatch record, and G-006 the physical attachment. No implication from a postulate to its own necessity is added.

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 fb2ce4548e60b84b6e8f0e72dd196c0347d2eb1b7e862d08650dab5aefdd8dd5

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-048 | 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