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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-e04e4f0adcd2298cccb7613e · master 4e63749e7f82b426 · S337.

LIB2-149 · The residual-circulation weights obey the printed piecewise rule

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.129 (bytes of record)):

ε5 = −φ−2 (the pentagon F -move coherence loop: the killed channel appears once, negative trace),

Statement

The registered residual trace weights are ε5 = −ϕ⁻², ε6 = 0 and εn = ϕ^(5−n) for n ≥ 7.

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 registered residual trace weights are ε5 = −ϕ⁻² (one claim)
p2 · ε6 = 0 (one claim)
p3 · εn = ϕ^(5−n) for n ≥ 7. (one claim)

Scope

carrier	The residual boundary-circulation weights in the finite n-gon quotient
domain	The three cases of the finite trace-selection rule.
hypotheses	Use the quotient and Markov trace of the composition ladder.; The pentagon, hexagon and higher-cell cases have the source's specified annular typing.
quantifier	The registered construction and its stated premises.

What this does not show. The piecewise weight rule does not by itself define a physical energy correction or justify an untyped change to a binding formula.

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, Pentagon residual trace — PDF p.133 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS

ε5 = −φ−2 (the pentagon F -move coherence loop: the killed channel appears once, negative trace),

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

ε6 = 0 (the hexagon’s two boundary orientations are mirror-paired in the annular quotient and cancel),

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

εn = φ 5−n (n ≥ 7) (exactly one noncontractible class survives, decaying φ−1 per added cell).

The text extraction above lost mathematical typography. Restored from the sealed TeX source (rev32.7/tex/p9_nuclear_cluster_tier.tex:239-241): εₙ=φ⁵⁻ⁿ (n≥7) (exactly one noncontractible class survives, decaying φ⁻¹ per added cell). (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	A1357; Paper 9 §6, residual trace selection rule, p.129	—	shipped	The three cases are printed together in the source; no fusion-path or annular trace calculation is rerun.

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
`5`	PDF p.129 (bytes of record)	closed form: the piecewise ε-selection rule printed in Paper 9 §6
`−2`	PDF p.129 (bytes of record)	closed form: the piecewise ε-selection rule printed in Paper 9 §6
`6`	PDF p.129 (bytes of record)	closed form: the piecewise ε-selection rule printed in Paper 9 §6
`0`	PDF p.129 (bytes of record)	closed form: the piecewise ε-selection rule printed in Paper 9 §6
`7`	PDF p.129 (bytes of record)	closed form: the piecewise ε-selection rule printed in Paper 9 §6

Typed links

type	target	licensed by
`related_to` (never evidential)	LIB2-148 The composition ladder is a finite trace invariant	—
`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 (3)
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	A1357
candidate ids (frozen list S304)	C2-077

Drafting-lane note

Selection-rule child of C2-077. All three printed cases are kept in one record; their application to energies remains the separate declared interface G-148.

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 fe0dccdd211bcf83c37e8d3c29da4d859a5f6566da031df2df98f94ce13e8fc3

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-149 | 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