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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-a479a6b41e99e6851ef83b7c · master 3fb7fca1ceb9ba49 · S337.

LIB2-117 · The edge-uniform parent metric has zero relative Yukawa rank

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.231 (bytes of record)):

The parent edge-residue map is rank 1 with relative rank 0: every channel sees the identical edge product

Statement

At the registered golden vacuum, the parent edge-residue map has rank 1 and relative rank 0 because all four Yukawa channels see the same product of edge-uniform positive metrics.

Parts of the statement (3)

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 parent edge-residue map has rank 1 (one claim)
p2 · relative rank 0 (one claim)
p3 · because all four Yukawa channels see the same product of edge-uniform positive metrics. (one claim)

Scope

carrier	The reflected cubic-cone kinetic metric and its three off-diagonal Peirce edges
domain	The edge-uniform two-derivative parent geometry, not arbitrary physical residues.
hypotheses	Use GAB = ∂A∂B[−log N] at the registered unit-norm golden vacuum.; Every loaded Yukawa vertex draws one field from each of the three Peirce edges.
quantifier	The registered construction and its stated hypotheses.
real form	J3(Os) with the registered reflected positive metric

What this does not show. The zero relative rank belongs to this parent geometry and does not exclude more general symmetry-breaking residues.

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 K, §3.6, Edge-uniform metrics — PDF p.242 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: grok read THE_RECORD → CONTEXT · gemini read SUITE_TEXT_EXTRACT → CONTEXT

On the three off-diagonal Peirce edges the reflected positive metrics are component-uniform scalars,

Appendix K, §3.6, Proposition 3.2: relative rank — PDF p.243 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS

The parent edge-residue map is rank 1 with relative rank 0: every channel sees the identical edge product

Appendix K, §3.6, Unresolved distinctions within an edge — PDF p.243 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: grok read THE_RECORD → CONTEXT · gemini read SUITE_TEXT_EXTRACT → CONTEXT

the edge-uniform parent geometry cannot resolve Q from L inside J13 nor uc , dc , ec , ν c inside J23 .

The text extraction above lost mathematical typography. Restored from the sealed TeX source (rev32.7/tex/appendix_k_yukawa_coefficient_negative.tex:175-176): the edge-uniform parent geometry cannot resolve Q from L inside J₁₃ nor u^c,d^c,e^c,ν^c inside J₂₃. (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
analytic	Appendix K §3.6, Proposition 3.2, p.231	—	shipped	The source displays the common edge-product argument; this is a restatement, not an independent metric derivation.
computational	A1052, parent-action metric check, Appendix K §3.6, p.231	—	unknown	The suite reports analytic-versus-finite-difference checks and a rerun; the code and output 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
`1`	PDF p.231 (bytes of record)	suite text p.231: parent rank 1 and relative rank 0 in Proposition 3.2
`0`	PDF p.231 (bytes of record)	suite text p.231: parent rank 1 and relative rank 0 in Proposition 3.2

Typed links

type	target	licensed by
`related_to` (never evidential)	LIB2-115 The unrestricted residue map can reproduce any positive Yukawa quartet	—

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 (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
Track-2 claim ids	C-RANK-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	A1052
candidate ids (frozen list S304)	C2-049

Drafting-lane note

C2-049 retains the two-derivative edge-uniform domain. It is not merged with the rank-four unconstrained residue map; no stronger universal parameter-count statement 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 74b1198234892e5f2219243fa0725534aea640c4d1129f33b453e193ac0fb8be

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-117 | 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