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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-5b0c45930e78cd1eb8ffd8d0 · master 7570ddad604d5b37 · S342.

LIB2-042 · A norm-only action leaves the regular norm-level directions flat

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.167 (bytes of record)):

for any C 2 action S = F (α, N (X)), stationarity at a regular norm-one point forces FN = 0 and hence Hess S ≡ 0 on ker dN , giving at least 26 flats structurally.

Statement

For a twice-differentiable norm-only action S = F(α,N(X)), ambient stationarity in X at a regular norm-one point forces Hess S to vanish on ker dN, leaving at least 26 flats.

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 · For a twice-differentiable norm-only action S = F(α,N(X)), ambient stationarity in X at a regular norm-one point forces Hess S to vanish on ker dN (one claim)
p2 · leaving at least 26 flats. (one claim)

Reviewer finding, ruled R79: A1637 F05 (R79-b): F_N = 0 follows from ambient X-stationarity; under stationarity constrained to N = 1 the constrained Hessian must be used. The qualifier “under ambient X-stationarity” joins this statement at REV32.12 (= Rev33.0, R156), with appendix_e_vacuum_selector.tex:247.

Scope

carrier	Regular norm-level tangent directions in the stated cubic carrier
domain	The norm-only action subclass, not general invariant or source-dependent actions.
hypotheses	S depends on X only through N(X), with the other argument α fixed.; The point is stationary, regular and norm-one.
quantifier	The declared class only.

What this does not show. The source check is on a generic symmetric cubic, not a dedicated full-Jordan computation, and the conclusion is limited to norm-only actions.

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(vi), Norm-only Hessian obstruction — PDF p.174 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS · grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS

for any C 2 action S = F (α, N (X)), ambient stationarity in X at a regular norm-one point forces FN = 0 and hence Hess S ≡ 0 on ker dN , giving at least 26 flats structurally.

Appendix E, §6(vi), Scope of the house check — PDF p.174 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → CONTEXT · grok read THE_RECORD → CONTEXT · gemini read SUITE_TEXT_EXTRACT → CONTEXT

the norm-only computation was checked on a generic symmetric cubic in R27 rather than on J3 (Os ) itself.

The text extraction above lost mathematical typography. Restored from the sealed TeX source (rev32.7/tex/appendix_e_vacuum_selector.tex:251-252): the norm-only computation was checked on a generic symmetric cubic in ℝ²⁷ rather than on J₃(𝕆ₛ) itself. (R87 house restoration: rendered from the tex, not the quote; the quote above is what the machine gate matched)

Evidence (availability is not outcome)

kind	reference	line / key	availability	note
registry	Appendix E §6(vi), norm-only companion result, p.167	—	shipped	The argument is stated in the supplied suite. The source says the house check used a generic symmetric cubic in R27, not J3(Os) itself.

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
`26`	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)	LIB2-041 A frame-free invariant does not select the ordered Peirce frame	—
`cited_by_section`	E-C04.1.claims-used (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0051
`cited_by_section`	E-C04.1.prior-art (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0057
`cited_by_section`	E-C04.1.sources-receipt (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0066

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
candidate ids (frozen list S304)	C2-102

Drafting-lane note

The norm-only companion of the ordered-frame obstruction is recorded separately because its hypothesis and evidence differ. C2-102 is the nearest selector candidate; no new computation is claimed.

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 0d50f5d03f3ab8dd4ec4e8ce1a2c210b81cf23aff57ce42a38b9a93816e4408a

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-042 | 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