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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-c756768a40bae00b9ffb0cd7 · master 742e6c24f3aa86af · S342.

LIB2-026 · A rank-character action represents the selector Hessian

class CLAIMmath status (as printed) Certifiedattachment (as printed) NOT_PRINTEDscorecard tier word (as printed) none printedhouse tier not yet assignedreview state PUBLISHEDentry version 11

Label sentence at the locator (PDF p.296 (bytes of record)):

no microscopic principle selects Fchar ; the mathematics is Derived/Certified, the attachment Structural/Conditional.

Statement

The registered rank-normalized carrier-character action Fchar has a critical point at the base with ∇²Fchar(I) = QT, and its displayed coefficients are traced to carrier ranks.

Parts of the statement (4)

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 rank-normalized carrier-character action Fchar has a critical point at the base with ∇²Fchar(I) = QT (cut further below)
p1-p1 · The registered rank-normalized carrier-character action Fchar has a critical point at the base (one claim)
p1-p2 · with ∇²Fchar(I) = QT (one claim)
p2 · its displayed coefficients are traced to carrier ranks. (one claim)

Scope

carrier	Loaded plane PB, Frobenius-orthonormal p-basis and joint-defect projectors
domain	The displayed action and its second variation, not a uniqueness theorem for actions.
hypotheses	PB = iB iBᵀ is the loaded plane.; The projectors Π1,Π32,Π36 and Ξ = Π10 − Π26 are the registered joint-defect projectors.; Fchar is the particular nonlinear functional printed in Theorem 9.1.
quantifier	The declared class only.
real form	Frozen split-real carrier

What this does not show. A variational representation of QT does not supply a microscopic principle selecting Fchar or its nonlinear shape.

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, §9.1, Theorem 9.1: critical point and Hessian — PDF p.313 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS

has its critical point at the base with ∇2 Fchar (I) = QT exactly

The text extraction above lost mathematical typography. Restored from the sealed TeX source (rev32.7/tex/appendix_s_selector_ledger.tex:688-689): has its critical point at the base with ∇²F_char(I)=Q_T exactly (R87 house restoration: rendered from the tex, not the quote; the quote above is what the machine gate matched)

Appendix S, §9.1, Rank-traced constants — PDF p.313 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS

Every constant is rank-traced: 16/27 = (24/27)(2/3), 1/27 = 1/r+ , 4/9 = (24/27)(1/2)

Appendix S, §9.1, Adopted theorem fence — PDF p.313 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: grok read THE_RECORD → CONTEXT · gemini read SUITE_TEXT_EXTRACT → CONTEXT

no microscopic principle selects Fchar ; the mathematics is Derived/Certified, the attachment Structural/Conditional.

Evidence (availability is not outcome)

kind	reference	line / key	availability	note
computational	s1052; A1515, Appendix S §9.1, p.296	—	unknown	The suite reports central finite differences of the actual nonlinear functional; no kernel or output is supplied here.

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.296 (bytes of record)	closed form: ∇2 Fchar(I) = QT in Theorem 9.1

Premises this record rests on (qualified uses)

Each row is a house-declared use of a registered premise (R37). DECLARED is the house's editorial judgment only; a use becomes REVIEWED when two non-drafting lanes, reading different objects, agree the premise is LOAD_BEARING for this record's result. REJECTED rows were retired by ruling and are shown for provenance.

use	state	premise	role	why the house declared it · reads
`USE-0004`	REJECTED by PI (R78)	PRM-007 (PRM-007/r1) — Action shape	adopted_physical	Hypotheses name 'the particular nonlinear functional printed in Theorem 9.1' and the domain says 'not a uniqueness theorem for actions' - it stands on the adopted action shape, not a derived one.

Typed links

type	target	licensed by
`depends_on`	LIB2-025 The loaded-plane defect algebra determines the selector eigenspaces	Appendix S p.296, Theorem 9.1 uses the zero-price joint-defect projectors of A1514 in constructing the carrier character and Fchar.
`cited_by_section`	E-C04.2.claims-used (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0072
`cited_by_section`	E-C04.2.derivation (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0119
`cited_by_section`	E-C04.2.prior-art (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0092
`cited_by_section`	E-C04.2.sources-receipt (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0142

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

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-F1b` A1632	PREDICATE	CLOSED 2026-09-17	Its target Q_T is the operator whose five-eigenspace construction A1632-F1 found incomplete as printed; the Hessian identity itself is not contradicted. How it was closed: R135 D-3 (PI, S342): consequential on A1632-F1, its only basis; the finding itself says the Hessian identity is not contradicted, and LIB2-026 claims only ∇²Fchar(I) = QT with coefficients traced to carrier ranks. All three uses REVIEWED with R49c pairs; no re-read.	as A1632-F1; s1051 G8 (H70 = Ptop_eta + (24/54)P32 + H36). paper: REV32.9_CHANGELOG S327·A1632 item 1 (landed in Rev32.9)	closed

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-RCHAR-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	A1515 s1052
candidate ids (frozen list S304)	C2-107

Drafting-lane note

The source's full mathematical phrase is Derived/Certified; the field retains its literal Certified token. Its attachment phrase Structural/Conditional is preserved in the quote but is not converted to Conditional-readout. scorecard_tier_word is null.

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 d4dd4615a4746e327c4f299e50cebf956c386c6804e44bd3d92a636fa5579360

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-026 | 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