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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-239a167772695a7dc8a7e7bf · master 512128af9fe79065 · S327.

LIB2-027 · The declared action-completion class retains nonlinear-shape freedom

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.297 (bytes of record)):

the solution set of “critical point at the base + positive-semidefinite Hessian” modulo equivalence is a four-dimensional moduli space,

Statement

In the declared rank-normalized character-completion class, actions with a critical point at the base and positive-semidefinite Hessian form, modulo equivalence, a four-dimensional moduli space: three Hessian-weight ratios and one nonlinear modulus invisible to the complete two-jet.

Scope

carrier	Nonlinear actions in the declared rank-normalized character-completion class
domain	The declared completion class before adopting Φdiag; not every possible action class.
hypotheses	Use the class and equivalence relation declared before the source analysis.; Require a critical point at the base and positive-semidefinite Hessian.
quantifier	The declared class only.

What this does not show. This obstruction is class-relative; enlarging the class changes its moduli count, and matching a Hessian alone does not select an action.

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 S, §9.4, Theorem 9.4: moduli space — PDF p.314 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS

the solution set of “critical point at the base + positive-semidefinite Hessian” modulo equivalence is a four-dimensional moduli space,

Appendix S, §9.4, Theorem 9.4: moduli decomposition — PDF p.314 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS

three Hessian-weight ratios plus one nonlinear modulus invisible to the complete two-jet.

Appendix S, §9.4, Same-Hessian nonlinear family — PDF p.314 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → CONTEXT · the lanes disagreed; resolved by PI ruling R74 as SUPPORTS — R74 (S327): the principal investigator ruled the six disputed readings of read round 1 (D1284/D1285); a use resolved by ruling never anchors PUBLISHED

Hence Fs = Fchar + s N is a continuous family of inequivalent bar-legal actions all with second variation exactly QT (house s1054, fd floor): exact Hessian agreement does not select the nonlinear action.

Evidence (availability is not outcome)

kind	reference	line / key	availability	note
computational	s1054; A1516, Appendix S §9.4, p.297	—	unknown	The moduli and two-jet results are source-reported; the kernel and output are not supplied here.

Typed links

type	target	licensed by
`related_to` (never evidential)	LIB2-026 A rank-character action represents the selector Hessian	—
`cited_by_section`	E-C04.2.claims-used (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0073
`cited_by_section`	E-C04.2.derivation (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0120
`cited_by_section`	E-C04.2.prior-art (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0093
`cited_by_section`	E-C04.2.sources-receipt (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0143

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

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-U2` A1632	UNSURE	UNSURE	The display S°/Eq ≅ ℝ × int Δ³ describes the regular (interior) stratum; zero-weight faces and degenerate PSD strata are not shown. The four-dimensional top-stratum count is not refuted.	appendix_s_selector_ledger.tex:761 (display confirmed by the house). paper: REV32.9_CHANGELOG S327·A1632 item 6 (landed in Rev32.9)	open question (UNSURE)

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	C-PHIDIAG-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	A1516 s1054
candidate ids (frozen list S304)	C2-108

Drafting-lane note

Moduli child of C2-108. The four-dimensional count belongs to this declared class; it is not substituted for the later enlarged-class five-modulus statement.

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 5ba75a403cc9ab5f826fd19ca3c8bee4731163dc8bc8756398cc983b5a1c8fa5

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-027 | 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