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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-bbc5539d192ed1d4e99e7bf7 · master 4e63749e7f82b426 · S337.

LIB2-145 · The small-nucleus kernel is triangularly saturated

class CLAIMmath status (as printed) NOT_PRINTEDattachment (as printed) NOT_PRINTEDscorecard tier word (as printed) none printedhouse tier not yet assignedreview state PUBLISHEDentry version 9

Label sentence at the locator (PDF p.128 (bytes of record)):

Freedom audit (carried verbatim): the rule introduced three new φ-coefficients and was scored on three new nuclei with a triangular dependency — zero net overdetermination within A ≤ 4, so no blind credit for the coefficient choice.

Statement

For A ≤ 4, three new phi coefficients were tested on three new nuclei with a triangular dependency, leaving zero net overdetermination and no blind credit for the coefficient choice.

Parts of the statement (6)

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 · three new phi coefficients were tested on three new nuclei with a triangular dependency (cut further below)
p1-p1 · three new phi coefficients were tested on three new nuclei (one claim)
p1-p2 · with a triangular dependency (one claim)
p2 · leaving zero net overdetermination and no blind credit for the coefficient choice. (cut further below)
p2-p1 · leaving zero net overdetermination (one claim)
p2-p2 · no blind credit for the coefficient choice (one claim)

Scope

carrier	The small-nucleus binding rule of Paper 9, Eq. (1)
domain	The A ≤ 4 calibration structure; later continuations carry the discriminating test.
hypotheses	Use the initial coefficient set and triangular dependency described in the freedom audit.
quantifier	The registered construction and its stated premises.

What this does not show. The initial fit does not independently predict the nuclei used to fix its coefficients or establish the later continuations.

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, §3, Small-nucleus freedom audit — PDF p.132 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS

Freedom audit (carried verbatim): the rule introduced three new φ-coefficients and was scored on three new nuclei with a triangular dependency — zero net overdetermination within A ≤ 4, so no blind credit for the coefficient choice.

Paper 9, §3, Continuation beyond the initial kernel — PDF p.132 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: grok read THE_RECORD → CONTEXT · gemini read SUITE_TEXT_EXTRACT → CONTEXT

The discriminating test was structural: A ≥ 5 has no new binomial available, and everything from §4 on is scored against that zero-freedom continuation.

Evidence (availability is not outcome)

kind	reference	line / key	availability	note
registry	A1349; Paper 9 §3, freedom audit, p.128	—	shipped	The supplied audit states the coefficient and target counts; this round does not refit coefficients or award blind credit.

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
`4`	PDF p.128 (bytes of record)	suite text p.128 only (no kernel line found)

Typed links

type	target	licensed by
`related_to` (never evidential)	LIB2-143 The exhibited winding-to-Fibonacci functor defines the finite cluster image	—

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

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-KER-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	A1349
candidate ids (frozen list S304)	C2-076

Drafting-lane note

C2-076 retains the triangular-saturation qualification. The status phrase sharp-pass-with-tongs is preserved only in the source, not converted to an unsupported tier.

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 9d596fc0706c97821760c5ec2c41365467b28f19e7a1d45a1a19851e0f4573d2

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-145 | 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