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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-04444d6ce8618cdd96b42255 · master cb9ce26d95e37a21 · S327.

LIB2-019 · Route A selects the positive golden spectrum under its stated hypotheses

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.164 (bytes of record)):

A real positive diagonal Jvac ∈ J3 (Os ) satisfying (H0)–(H2) is unique up to permutation:

Statement

A positive real diagonal Jvac satisfying unit determinant, inversion symmetry and DET-7 has spectrum {ϕ,1,ϕ⁻¹}, unique up to permutation.

Scope

carrier	Positive real diagonal Jvac in J3(Os)
domain	Appendix E Route A; no number-field restriction is used.
hypotheses	H0: Det(Jvac) = 1.; H1: Jvac is isospectral to its Jordan adjoint; at unit determinant this is inversion symmetry.; H2: det Gram(Jvac,Jvac#) = 7.
quantifier	Every positive real diagonal element satisfying H0–H2.
real form	J3(Os)

What this does not show. The theorem selects a spectral orbit only; it neither derives DET-7 nor selects an ordered physical Peirce frame.

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 E, §3, Theorem 1: symmetry-form selector — PDF p.170 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS

A real positive diagonal Jvac ∈ J3 (Os ) satisfying (H0)–(H2) is unique up to permutation:

Appendix E, §3, Theorem 1: spectral conclusion — PDF p.170 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS

Thus the spectrum is {ϕ, 1, ϕ−1 }, unique up to permutation.

The text extraction above lost mathematical typography. Restored from the sealed TeX source (rev32.7/tex/appendix_e_vacuum_selector.tex:90): Thus the spectrum is {ϕ,1,ϕ⁻¹}, unique up to permutation. (R87 house restoration: rendered from the tex, not the quote; the quote above is what the machine gate matched)

Appendix E, §9, Ordered-frame boundary — PDF p.179 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: grok read THE_RECORD → CONTEXT · gemini read SUITE_TEXT_EXTRACT → CONTEXT

The ordered physical Peirce frame remains loaded: a frame-free F4 -invariant selects only the spectral orbit (item (vi), s978/s981), so ordering requires a loading or symmetry-breaking tensor.

Evidence (availability is not outcome)

kind	reference	line / key	availability	note
analytic	Appendix E §3, Lemma 2 and Theorem 1, pp.164–165	—	shipped	The selector argument is printed in the supplied text; this record restates it without a new proof audit.

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.164 (bytes of record)	closed form: H2 and the spectral conclusion of Theorem 1
`1`	PDF p.164 (bytes of record)	closed form: H2 and the spectral conclusion of Theorem 1
`−1`	PDF p.164 (bytes of record)	closed form: H2 and the spectral conclusion of Theorem 1

Premises this record rests on (qualified uses)

Each row is a house-declared use of a registered premise (R37). DECLARED is the house's editorial judgment only; a use becomes REVIEWED when two non-drafting lanes, reading different objects, agree the premise is LOAD_BEARING for this record's result. REJECTED rows were retired by ruling and are shown for provenance.

use	state	premise	role	why the house declared it · reads
`USE-0017`	REVIEWED by lanes (R49c)	PRM-013 (PRM-013/r1) — DET-7 structural postulate	hypothetical_assumption	DET-7 enters Route A as a HYPOTHESIS of the theorem (H2), not as a postulate the programme adopts about nature. Same assertion as LIB2-018 uses, different role. gemini · LOAD_BEARING · SUITE_TEXT_EXTRACT (D1350) grok · LOAD_BEARING · THE_RECORD (D1349)
`USE-0018`	REVIEWED by lanes (R49c)	PRM-023 (PRM-023/r1) — Route A inversion symmetry (palindromic spectrum)	hypothetical_assumption	Route A additionally assumes adjoint isospectrality / inversion symmetry. This is what distinguishes its theorem domain from Route B, and it is invisible in the dependency edges, which are identical. gemini · LOAD_BEARING · SUITE_TEXT_EXTRACT (D1350) grok · LOAD_BEARING · THE_RECORD (D1349)

Typed links

type	target	licensed by
`uses_input`	LIB2-018 DET-7 is a structural postulate in the algebraic selector	Appendix E pp.163–164: H2 is DET-7, and Theorem 1 explicitly assumes H0–H2.
`rests_on_premise`	PRM-013 DET-7 structural postulate	—
`rests_on_premise`	PRM-023 Route A inversion symmetry (palindromic spectrum)	—
`cited_by_section`	E-C04.1.claims-used (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0048
`cited_by_section`	E-C04.1.prior-art (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0053
`cited_by_section`	E-C04.1.sources-receipt (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0063

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	A-VAC-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	A641
candidate ids (frozen list S304)	C2-102

Drafting-lane note

Symmetry-route child of C2-102. Its hypotheses differ from the arithmetic route G-024 and are not merged merely because their spectra agree. No scorecard tier is inferred from Theorem 1.

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 45087f33b267c3a0bf1f5263a6eb47481f9a1a405f3e2d8656d3eeb52b15a560

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-019 | 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