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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-fff6de862fd8462f40c8718c · master 742e6c24f3aa86af · S342.

LIB2-021 · The finite loaded-profile parent action has its stated stable minimum

class CLAIMmath status (as printed) NOT_PRINTEDattachment (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.170 (bytes of record)):

Complete-conditional, selector tier. Within the frozen split-real 56-frame and the declared finite/internal loaded-profile class: the selector parent action Vtotal has its global minimum at (j ∗ , q ∗ = 32 j ∗ , M ∗ = I) with combined Hessian positive for all ρ, u0 , κd > 0 and [W0 ] the exact projective soft ray at zero inserted dark amplitude.

Statement

Within the frozen split-real 56-frame and declared finite/internal loaded-profile class, Vtotal attains its stated global minimum at M* = I and the displayed source-aligned pair (j*,q*), with combined Hessian positive for every ρ,u0,κd > 0 on the directions transverse to the exact projective soft ray [W0] at zero inserted dark amplitude, along which it vanishes.

Parts of the statement (2)

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 · Vtotal attains its stated global minimum at M* = I and the displayed source-aligned pair (j*,q*) (one claim)
p2 · with combined Hessian positive for every ρ,u0,κd > 0 on the directions transverse to the exact projective soft ray [W0] at zero inserted dark amplitude, along which it vanishes. (one claim)

Scope

carrier	Finite/internal loaded-profile selector in the frozen real V56
domain	Configuration-space minimum and stability, not the velocity Hessian used in the Legendre step.
hypotheses	The loaded boundary datum and assembled selector action are supplied.; ρ,u0,κd are positive; no numerical values are fixed.
quantifier	All positive parameters in the declared class.
real form	Split-real 56-frame

What this does not show. This finite configuration-space closure is not a continuum Hamiltonian or an interacting pole/LSZ construction.

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 E, §7, Closure declaration: minimum and Hessian — PDF p.177 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS

the selector parent action Vtotal has its global minimum at (j ∗ , q ∗ = 32 j ∗ , M ∗ = I) with combined Hessian positive for all ρ, u0 , κd > 0 on the directions transverse to [W0 ], the exact projective soft ray at zero inserted dark amplitude, along which it vanishes (scope stated Rev32.9, A1632).

Appendix E, §7, Corrected Hessian typing — PDF p.175 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: grok read THE_RECORD → CONTEXT · gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → CONTEXT · gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → CONTEXT · gemini read SUITE_TEXT_EXTRACT → CONTEXT

the Hessian that enters the Legendre step is the velocity Hessian I32 /U — a different object from the A1506 configuration Hessian, which is a stability record only; conflating the two mis-types the attachment.

Appendix E, §7, Closure declaration: physical boundary — PDF p.177 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: grok read THE_RECORD → CONTEXT · gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → CONTEXT · gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → CONTEXT · gemini read SUITE_TEXT_EXTRACT → CONTEXT

Fences: this closes the finite/internal loaded-profile selector only — continuum, pole, and LSZ remain a separately typed frontier;

Evidence (availability is not outcome)

kind	reference	line / key	availability	note
registry	A1509 Theorem C; A1510/A1511 confirmations, Appendix E §7, p.170	—	shipped	The supplied suite reports the closure; original referee returns and numerical payloads are not 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
`56`	PDF p.170 (bytes of record)	suite text p.170: frozen 56-frame and positive-parameter condition; no kernel line found
`0`	PDF p.170 (bytes of record)	suite text p.170: frozen 56-frame and positive-parameter condition; no kernel line found

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-0023`	REVIEWED by lanes (R49c)	PRM-010 (PRM-010/r1) — Boundary datum	hypothetical_assumption	Proposed by the drafting lane (A1634): The source explicitly identifies this datum as what the action is conditional on. The record’s finite/internal global-minimum statement is the loaded-profile selector result, not an intrinsic choice of this boundary. — House reading: House read App E:307–312: "The datum the action is conditional on is single"; LIB2-021 states the minimum of that action within the declared class at the source-aligned pair (j,q). The premise is a hypothesis of the stated result. gemini · LOAD_BEARING · SUITE_TEXT_EXTRACT (D1350) grok · LOAD_BEARING · THE_RECORD (D1349)

Typed links

type	target	licensed by
`cited_by_section`	E-C04.2.claims-used (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0067
`cited_by_section`	E-C04.2.derivation (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0114
`cited_by_section`	E-C04.2.prior-art (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0090
`cited_by_section`	E-C04.2.sources-receipt (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0137
`rests_on_premise`	PRM-010 Boundary datum	appendix_e_vacuum_selector.tex:308 — "The datum the action is conditional on is single: $[j]\;\Longleftrightarrow\; L_\partial\;\Longleftrightarrow\;E^{*}=\operatorname{span}\{i_Bj,\;\Omega i_Bj\}$"

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 (1)
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-U1` A1632	UNSURE	UNSURE	A positive combined Hessian is printed beside an exact projective soft ray; the tangent space or quotient on which positivity holds is not stated.	Thm C closure box, appendix_e. paper: REV32.9_CHANGELOG S327·A1632 item 6 (landed in Rev32.9)	open question (UNSURE)
`A1632-F3c` A1632	QUOTE_RENDERING	CONFIRMED	The quote reads 'q=32 j'; the source prints q* = (3/2) j*.	appendix_e closure box (q^{}=\tfrac32 j^{}).	no — the predicate is unaffected
`A1711-F01` A1711	PREDICATE	CLOSED 2026-09-17	The R130 statement dropped the printed qualifier: the soft ray [W0] is the projective soft ray at zero inserted dark amplitude. How it was closed: R135 D-2 (PI, S342): R132 D-1 re-type applied and all three LIB2-021 uses REVIEWED in round 23 (A1715/A1716).	SUITE_TEXT_S341 p.174 (App E closure declaration)	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-PAR-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	A1506 A1509 A1510 A1511
candidate ids (frozen list S304)	C2-105

Drafting-lane note

Minimum/Hessian child of C2-105. The source-aligned pair is specified by the quoted declaration; the flattened fraction in that quote is not repaired or used to generate a new number. The source's complete-conditional phrase is not converted to Conditional-readout.

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 ded57726ab8a0d82c2cb7e4449fb531e4f1726d205f11f1630594cf9e382dff9

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-021 | 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