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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-c4490854ca62f1b0ee0258f1 · master 4e63749e7f82b426 · S337.

LIB2-137 · The cone expansion uses a spectral background rather than stationarity of the cubic

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.209 (bytes of record)):

which is why the expansion is organized by the Hessian spectrum rather than by a stationary phase.

Statement

The source organizes the cone expansion at Jvac by the Hessian spectrum rather than stationary phase of N, because ∇N ≠ 0 there.

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 · The source organizes the cone expansion at Jvac by the Hessian spectrum rather than stationary phase of N (one claim)
p2 · because ∇N ≠ 0 there. (one claim)

Scope

carrier	The cone-Hessian expansion about the registered spectral background
domain	The spectral-background interpretation of this expansion, not the full gauged-potential stability question.
hypotheses	Use the cubic norm N and the Hessian G in Appendix I, Remark 6.4.
quantifier	The registered construction and its stated hypotheses.
real form	The registered cubic-norm cone

What this does not show. This expansion prescription does not establish a stationary or stable vacuum of a different gauged or sourced action.

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 I, §6, Remark 6.4(i): spectral background — PDF p.219 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS

The vacuum is a spectral background, not a saddle: Jvac is selected by the eigenvalue structure of G, not by ∇N = 0 (indeed ∇N = ̸ 0 there),

Appendix I, §6, Remark 6.4(i): expansion principle — PDF p.219 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS

which is why the expansion is organized by the Hessian spectrum rather than by a stationary phase.

Appendix I, §6, Remark 6.4: normalization boundary — PDF p.219 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: grok read THE_RECORD → CONTEXT · gemini read SUITE_TEXT_EXTRACT → CONTEXT

the legacy vacuum normalization diag(ϕ2 , 1, 0) is superseded by the current {ϕ, 1, ϕ−1 } frame, the structural statements unaffected.

The text extraction above lost mathematical typography. Restored from the sealed TeX source (rev32.7/tex/appendix_i_dynamics_bounce.tex:502-504): the legacy vacuum normalization diag(ϕ²,1,0) is superseded by the current {ϕ,1,ϕ⁻¹} frame, the structural statements unaffected. (R87 house restoration: rendered from the tex, not the quote; the quote above is what the machine gate matched)

Evidence (availability is not outcome)

kind	reference	line / key	availability	note
registry	L-SpectralBackground; Appendix I §6, Remark 6.4(i), p.209	—	shipped	The current suite supplies the spectral-background sentence; the original house-file body is 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
`0`	PDF p.209 (bytes of record)	suite text p.209: ∇N is nonzero in Remark 6.4(i)

Typed links

type	target	licensed by
`related_to` (never evidential)	LIB2-135 The spectral-gap model imposes its self-consistency through the lifted cone trace	—

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
candidate ids (frozen list S304)	C2-171

Drafting-lane note

C2-171 is recovered in the source’s spectral-background sense. Its title is not exported into a blanket statement that every potential has no saddle at the named vacuum.

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 931e354fda7fde3f4cb37fc5af47db13fc0f09e6815e6dab401f6e3702d5d32f

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-137 | 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