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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-544d06543781c6c45f1eee14 · master 4e63749e7f82b426 · S337.

LIB2-148 · The composition ladder is a finite trace invariant

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.129 (bytes of record)):

Tn = (n − 2) + εn , εn = trϕ (Rn )

Statement

The finite composition weights obey Tn = (n − 2) + εn with εn = trϕ(Rn), where the trace is taken on the residual boundary-circulation class in the stated Temperley–Lieb quotient.

Scope

carrier	The n-gon flip graph and residual boundary-circulation class
domain	The finite trace weight, before its declared binding-energy attachment.
hypotheses	Use the quotient TLφ/⟨f4⟩ and its registered Markov trace.
quantifier	The registered construction and its stated premises.

What this does not show. The finite trace law does not on its own derive a binding energy or a continuum Yang–Mills functor.

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.

Paper 9, §6, Equation (3): trace ladder — PDF p.133 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS

Tn = (n − 2) + εn , εn = trϕ (Rn )

Paper 9, §6, Meaning of the trace — PDF p.133 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS

where (n − 2) counts the triangle slots in any pants decomposition of the n-gon and εn is the Markov trace of the residual boundary-circulation class of the n-gon flip graph in the Temperley–Lieb quotient TLφ /⟨f4 ⟩.

Paper 9, §6, Weight versus energy — PDF p.133 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: grok read THE_RECORD → CONTEXT · gemini read SUITE_TEXT_EXTRACT → CONTEXT

the identity prices a weight, not an energy

Evidence (availability is not outcome)

kind	reference	line / key	availability	note
registry	A1356/A1357; Paper 9 §6, Eq. (3), p.129	—	shipped	The source prints the trace law and its domain; the underlying trace calculations are not supplied as executable artifacts.

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
`2`	PDF p.129 (bytes of record)	closed form: Tn = (n − 2) + εn and εn = trϕ(Rn), Paper 9 Eq. (3)

Typed links

type	target	licensed by
`related_to` (never evidential)	LIB2-143 The exhibited winding-to-Fibonacci functor defines the finite cluster image	—
`related_to` (never evidential)	LIB2-144 The cluster-ledger interface is the declared weight-to-energy map	—

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	E-LAD-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	A1356 A1357
candidate ids (frozen list S304)	C2-077

Drafting-lane note

Trace-law child of C2-077. The trace selection rule and the two source-reported vault matches are distinct records with their own evidence.

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 193fbb8203b218b098f4475e0d192dc59f277ae3aef800a16d625ce616f0bc63

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-148 | 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