Claims & Evidence Registrar › H03
Label sentence at the locator (PDF p.165 (bytes of record)):
ϕ2 + ϕ−2 = 3,
The selected golden spectrum satisfies the exact internal identity ϕ² + ϕ⁻² = 3.
| carrier | The positive golden vacuum spectrum |
|---|---|
| domain | The exact spectral identity, distinct from its solar-angle application. |
| hypotheses | The vacuum has the selected spectrum {ϕ,1,ϕ⁻¹}. |
| quantifier | The registered construction only. |
| real form | J3(Os) |
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.
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, §5, Corollary 1: spectral identity — PDF p.172 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS
ϕ2 + ϕ−2 = 3,
Appendix E, §9, Conditional-selector hypotheses — PDF p.179 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → CONTEXT
Theorems 1 and 2 discharge the carried item [A641/Q5A]: the working vacuum spectrum {ϕ, 1, ϕ−1 } is forced up to permutation, conditional on the named hypotheses (unit norm; inversion symmetry, or the golden-field restriction; DET-7), with the residual input named in each route.
| kind | reference | line / key | availability | note |
|---|---|---|---|---|
| analytic | Appendix E §5, Corollary 1, p.165 | — | shipped | The identity is printed as a spectral corollary; no independent algebraic calculation is performed. |
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 |
|---|---|---|
2 | PDF p.165 (bytes of record) | closed form: ϕ2 + ϕ−2 = 3 printed in Corollary 1 |
−2 | PDF p.165 (bytes of record) | closed form: ϕ2 + ϕ−2 = 3 printed in Corollary 1 |
3 | PDF p.165 (bytes of record) | closed form: ϕ2 + ϕ−2 = 3 printed in Corollary 1 |
| type | target | licensed by |
|---|---|---|
related_to (never evidential) | LIB2-019 Route A selects the positive golden spectrum under its stated hypotheses | — |
related_to (never evidential) | LIB2-020 Route B selects the positive golden-unit triple under DET-7 | — |
cited_by_section | E-C05.1.claims-used (Exposition section page; use UNREVIEWED) | TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0160 |
cited_by_section | E-C05.1.prior-art (Exposition section page; use UNREVIEWED) | TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0176 |
| 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 |
| 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 |
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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.
| March library (v1) antecedents | no legacy antecedent identified |
|---|---|
| candidate ids (frozen list S304) | C2-001 |
C2-001 imports an Axiom label, but this locator prints a corollary, not a scorecard label. Both literal source axes remain NOT_PRINTED. No March title is used as an exact antecedent.
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 94f73d745a891bd21314af18246963779b6c82173b8bed947fdb0d303b08e814
Reviewer verdict line (one per entry, as text): LIB2-046 | 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