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 4 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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-3a23fc5691332d22936a5343 · master 1aa73892adc5691e · S364.

LIB2-058 · The cubic scaling model has a constant homogeneity derivative

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.208 (bytes of record)):

Proposition 6.1 (the overall coupling does not run: βc = −9 by homogeneity).

Statement

For the scaling action S = c N(J) on J3(Os), the substitution J → c^{1/3}J gives, formally, Z(c) = c⁻⁹ Z(1) and c d(log Z(c))/dc = −9; the identity holds only for a regulator or integration domain that respects the scaling.

Scope

carrier	The cubic-norm scaling model on J3(Os)
domain	The bare-coupling homogeneity identity.
hypotheses	Use the source's scaling action and its formal partition-function normalization.; The real carrier dimension is 27 and the norm has degree 3.
quantifier	The stated scaling model.
real form	J3(Os)

What this does not show. This bare scaling identity does not determine the running of physical masses, which the source assigns to composite correlators.

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, Proposition 6.1: scaling setup — PDF p.218 (bytes of record)
review state: LANE_PROPOSED · role CONTEXT · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS · grok read THE_RECORD → CONTEXT · gemini read SUITE_TEXT_EXTRACT → CONTEXT

For the scaling action S = c N (J) on J3 (Os ) (dimR = 27, deg N = 3)

Appendix I, §6, Proposition 6.1: homogeneity factor — PDF p.218 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS · grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS

the substitution J → c1/3 J gives, formally, Z(c) = ec N dJ = c−9 Z(1),

Appendix I, §6, Proposition 6.1: constant derivative — PDF p.218 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS · grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS

c log Z(c) = − = −9, dc deg N constant in c. The integral does not converge on the real 27-dimensional space for either sign of c (N is odd), so the identity holds only for a regulator or integration domain that respects the scaling

Appendix I, §6, Physical-mass boundary — PDF p.218 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → CONTEXT · grok read THE_RECORD → CONTEXT · gemini read SUITE_TEXT_EXTRACT → CONTEXT

(Retyped Rev32.9, A1641 F01: through Rev32.8 this was titled “the overall coupling does not run: βc = −9” and concluded that running must come from composite correlators.

Evidence (availability is not outcome)

kind	reference	line / key	availability	note
registry	Appendix I §6, Proposition 6.1, p.208; L-BetaCTrivial	—	shipped	The source prints this as a homogeneity identity. The original L-file and a calculation of composite correlators 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
`3`	PDF p.208 (bytes of record)	closed form: J3(Os), c−9 Z(1), and βc = −9 printed in Proposition 6.1
`−9`	PDF p.208 (bytes of record)	closed form: J3(Os), c−9 Z(1), and βc = −9 printed in Proposition 6.1
`1`	PDF p.208 (bytes of record)	closed form: J3(Os), c−9 Z(1), and βc = −9 printed in Proposition 6.1

Why this record is PUBLISHED (R67, condition T-B)

states a predicate	yes
uses on the record · unblocked	4 · 4
uses any lane has read	4 of 4
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

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?
`A1711-F04` A1711	PROOF	CONFIRMED	App I Prop. 6.1 prints Z(c) = c^-9 Z(1) without a sign branch; for c < 0 the real substitution gives \|c\|^-9. The record repeats the paper and says "formally".	SUITE_TEXT_S341 p.212; appendix_i (Prop. 6.1) paper: REV32.10 S342.1	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
candidate ids (frozen list S304)	C2-144

Drafting-lane note

Source-recovered C2-144, restricted to the printed homogeneity relation and the source's definition of βc. The extraction displaces integral and derivative symbols; source quotations retain that layout. No convergent partition-function construction or physical running calculation 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 cd946e39739d36f86bdc0246fce623e829c919fc69c941d2e9efab74077eb62d

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-058 | 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