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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-1befcfc325b16879cb7264f2 · master 512128af9fe79065 · S327.

LIB2-015 · The golden braid-word square root on the frozen carrier

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.198 (bytes of record)):

is an exact symplectic unimodular square root of the braid word, Hϕ2 = Wh , with spectrum spec Hϕ = φ−1 (12) ⊕ 1(32) ⊕ φ+1 (12)

Statement

In the frozen 56-frame, the braid hyperbolic word Wh has an exact symplectic unimodular square root Hϕ with Hϕ² = Wh and eigenvalues φ⁻¹, 1 and φ of multiplicities 12, 32 and 12.

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 braid hyperbolic word Wh has an exact symplectic unimodular square root Hϕ with Hϕ² = Wh (one claim)
p2 · eigenvalues φ⁻¹, 1 and φ of multiplicities 12, 32 and 12. (one claim)

Scope

carrier	Frozen real 56-frame and its braid hyperbolic word
domain	Appendix H §11, the algebraic square-root construction.
group	Sp(V56)
hypotheses	Wh, P, Q and the Clifford generators are those of the frozen representation.; The source sets A = Wh − Q with A² − 3A + P = 0.
quantifier	The specified braid word in the frozen frame.
real form	Real symplectic carrier

What this does not show. This finite spectral construction does not attach the braid word to a physical mass, an absolute energy scale or an occupied winding level.

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 H, §11, Theorem 11.1: frozen-word setup — PDF p.205 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: grok read THE_RECORD → CONTEXT · gemini read SUITE_TEXT_EXTRACT → SUPPORTS · the lanes disagreed; resolved by PI ruling R74 as CONTEXT — R74 (S327): the principal investigator ruled the six disputed readings of read round 1 (D1284/D1285); a use resolved by ruling never anchors PUBLISHED

Within the frozen 56-frame let Wh = Q + 32 P + 32 γ1 − γ2 be the braid hyperbolic word and set A = Wh − Q, so that A2 − 3A + P = 0.

The text extraction above lost mathematical typography. Restored from the sealed TeX source (rev32.7/tex/appendix_h_time_bridge.tex:533-534): Within the frozen 56-frame let Wₕ=Q+(3/2)P+(3/2)γ₁-γ₂ be the braid hyperbolic word and set A=Wₕ-Q, so that A²-3A+P=0. (R87 house restoration: rendered from the tex, not the quote; the quote above is what the machine gate matched)

Appendix H, §11, Theorem 11.1: square root and spectrum — PDF p.206 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS

is an exact symplectic unimodular square root of the braid word, Hϕ2 = Wh , with spectrum spec Hϕ = φ−1 (12) ⊕ 1(32) ⊕ φ+1 (12)

The text extraction above lost mathematical typography. Restored from the sealed TeX source (rev32.7/tex/appendix_h_time_bridge.tex:538-541): is an exact symplectic unimodular square root of the braid word, H_ϕ²=Wₕ, with spectrum spec H_ϕ = φ^(-1 (12)) ⊕ 1⁽³²⁾ ⊕φ^(+1 (12)) (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
computational	s1047–s1050; A1512–A1513, Appendix H §11, p.198	—	unknown	The suite reports this computation; the kernel and its output are not supplied in this round.

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
`56`	PDF p.198 (bytes of record)	suite text p.198 only (no kernel line found)
`2`	PDF p.198 (bytes of record)	closed form: Hϕ2 = Wh printed in Theorem 11.1
`−1`	PDF p.198 (bytes of record)	closed form: φ−1 eigenvalue printed in the spectrum of Hϕ
`1`	PDF p.198 (bytes of record)	closed form: unit eigenvalue printed in the spectrum of Hϕ
`12`	PDF p.198 (bytes of record)	closed form: multiplicities in the displayed spectrum of Hϕ
`32`	PDF p.198 (bytes of record)	closed form: multiplicity of the unit eigenvalue in the displayed spectrum of Hϕ

Typed links

type	target	licensed by
`related_to` (never evidential)	LIB2-014 The active braid carrier consists of twelve Clifford-module copies	—
`cited_by_section`	E-C05.2.claims-used (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0187
`cited_by_section`	E-C05.2.prior-art (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0195
`cited_by_section`	E-C05.2.sources-receipt (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0208

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

Referee findings (R73)

Raised by a lane acting as referee and re-measured by the house before being listed (a lane's word alone is not a finding). Only a CONFIRMED finding against the record's predicate blocks PUBLISHED; the others are printed so a reader sees them.

finding	scope	state	what	evidence	affects this record's predicate?
`A1632-F3d` A1632	QUOTE_RENDERING	CONFIRMED	The quote reads 'Wh = Q + 32 P + 32 γ1 − γ2'; the source prints Wh = Q + (3/2)P + (3/2)γ₁ − γ₂.	appendix_h_time_bridge.tex:533.	no — the predicate is unaffected
`A1632-F3e` A1632	QUOTE_RENDERING	CONFIRMED	Use 2's quote begins mid-sentence ("is an exact symplectic unimodular square root…") and drops its subject, the defining display Hϕ = Q + (A+P)/√5 printed immediately before it on p.198.	sealed extract p.198 (house-located: the omitted display precedes the quote).	no — the predicate is unaffected

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-GBR-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	A1512 A1513 s1047 s1048 s1049 s1050
candidate ids (frozen list S304)	C2-104

Drafting-lane note

The square-root construction and its spectral multiset form one record. Quotes preserve the extraction's formula layout; no decimal approximation of φ is computed. The theorem heading is not copied into scorecard_tier_word.

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 db97b610554c7278b97a6640cd097c96b114a1b5b40b2924592c8a33d85ce8aa

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-015 | 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