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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-7adc412c7e27b2da3a8487cf · master ac37c14788254b3d · S327.

LIB2-043 · Unshifted quadratic Kempf–Ness potentials fail the selector-rank test

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.167 (bytes of record)):

rank Hess0 ∥µK ∥2 ≤ dim K ≤ 63 < 69 = rank QT (the rank no-go)

Statement

In the declared unshifted zero-level quadratic-carrier Kempf–Ness class, rank Hess0∥µK∥² ≤ dim K ≤ 63 < 69 = rank QT, so this class cannot reproduce the selector Hessian.

Scope

carrier	The unshifted zero-level quadratic carrier and its moment-map-square potential
domain	The unshifted zero-level quadratic-carrier class only.
group	K in the declared class
hypotheses	Use the predeclared Kempf–Ness class cited in Appendix E §6(vii).; The target is the registered selector Hessian QT.
quantifier	The declared class only.

What this does not show. Central shifts on proper subgroups or departure from the declared carrier/potential class are not excluded by this bound.

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, §6(vii), Unshifted Kempf–Ness rank bound — PDF p.174 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS

rank Hess0 ∥µK ∥2 ≤ dim K ≤ 63 < 69 = rank QT (the rank no-go)

The text extraction above lost mathematical typography. Restored from the sealed TeX source (rev32.7/tex/appendix_e_vacuum_selector.tex:258-259): rank Hess₀‖μ_K‖²≤ dim K≤ 63<69=rank Q_T (the rank no-go) (R87 house restoration: rendered from the tex, not the quote; the quote above is what the machine gate matched)

Appendix E, §6(vii), Declared class — PDF p.174 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → CONTEXT · the lanes disagreed; resolved by PI ruling R80 as CONTEXT — R80 (S327): the principal investigator ruled the four disputed readings of read round 2 (D1289/D1290); a use resolved by ruling never anchors PUBLISHED

For the class of Kempf–Ness potentials built on an unshifted zero-level quadratic carrier — declared before the run (class sha 6ece8dc9...)

Evidence (availability is not outcome)

kind	reference	line / key	availability	note
registry	A1512 Ask-2, Appendix E §6(vii), p.167	—	shipped	The rank obstruction is reported in the supplied suite; the class declaration and original computation 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
`0`	PDF p.167 (bytes of record)	suite text p.167: Hess0 basepoint label
`2`	PDF p.167 (bytes of record)	closed form: the moment-map squared norm in the rank bound
`63`	PDF p.167 (bytes of record)	suite text p.167 only (no kernel line found)
`69`	PDF p.167 (bytes of record)	suite text p.167 only (no kernel line found)

Typed links

type	target	licensed by
`related_to` (never evidential)	LIB2-027 The declared action-completion class retains nonlinear-shape freedom	—
`cited_by_section`	E-C04.2.claims-used (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0087
`cited_by_section`	E-C04.2.derivation (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0111, CIT-0134
`cited_by_section`	E-C04.2.prior-art (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0101
`cited_by_section`	E-C04.2.sources-receipt (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0157

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
serials	A1512
candidate ids (frozen list S304)	C2-108

Drafting-lane note

The rank and beat-transitivity obstructions have different mechanisms and are separate records. This source-printed action-class exclusion is associated with C2-108; it does not contradict the finite conditional closure.

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 aaf434e33d4198b90c2d62901d11f78c9252c172d75b205a614feee63ab8cd3a

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-043 | 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