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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-6c7a3b9efa6d977ccff7cc37 · master 7570ddad604d5b37 · S342.

LIB2-041 · A frame-free invariant does not select the ordered Peirce frame

class CLAIMmath status (as printed) NOT_PRINTEDattachment (as printed) NOT_PRINTEDscorecard tier word (as printed) none printedhouse tier not yet assignedreview state PUBLISHEDentry version 12

Label sentence at the locator (PDF p.167 (bytes of record)):

a frame-free F4 -invariant can at best select the spectral orbit [Jvac ]F4 ; it can never isolate the ordered frame diag(φ, 1, φ−1 ).

Statement

A frame-free F4-invariant can at best select the spectral orbit of Jvac, not its ordered frame; at a stationary point on the registered orbit it has at least 24 Hessian zero modes.

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 · A frame-free F4-invariant can at best select the spectral orbit of Jvac, not its ordered frame (cut further below)
p1-p1 · A frame-free F4-invariant can at best select the spectral orbit of Jvac (one claim)
p1-p2 · not its ordered frame (one claim)
p2 · at a stationary point on the registered orbit it has at least 24 Hessian zero modes. (one claim)

Reviewer finding, ruled R79: A1637 F05 (R79-b): the flat directions are Hessian zero modes at a stationary orbit; an orbit-invariant action need not have them at a nonstationary point. The qualifier “at a stationary orbit” joins this statement at REV32.12 (= Rev33.0, R156), with appendix_e_vacuum_selector.tex:241.

Scope

carrier	The ordered triple and its automorphism orbit
domain	Ordered-frame selection in the declared invariant class.
group	F4 automorphism action as printed
hypotheses	The scalar is invariant under the frame-free F4 automorphism action as printed.; The source identifies a 24-dimensional orbit of the ordered triple.
quantifier	The declared class only.

What this does not show. Selecting an ordered frame requires a loading or symmetry-breaking tensor; this result does not exclude selection with that additional datum.

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), Frame-free orbit 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

a frame-free F4 -invariant can at best select the spectral orbit [Jvac ]F4 ; it can never isolate the ordered frame diag(φ, 1, φ−1 ).

The text extraction above lost mathematical typography. Restored from the sealed TeX source (rev32.7/tex/appendix_e_vacuum_selector.tex:242-244): a frame-free F₄-invariant can at best select the spectral orbit [J_vac]_(F₄); it can never isolate the ordered frame diag(φ,1,φ⁻¹). (R87 house restoration: rendered from the tex, not the quote; the quote above is what the machine gate matched)

Appendix E, §6(vi), Orbit dimension — PDF p.173 (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

The stabilizer of the ordered triple inside the automorphism group leaves a 24-dimensional orbit, hence, at a stationary point on that orbit, at least 24 Hessian zero modes (flat directions) for any frame-free invariant

Evidence (availability is not outcome)

kind	reference	line / key	availability	note
registry	Appendix E §6(vi), p.167; s978/s981 are the stated count checks	—	shipped	The source attributes the theorem to the lane; the house checked dimension counts and accepted orbit invariance as standard rather than proving it here.
computational	s978/s981, dimension-count checks cited in Appendix E §6(vi), p.167	—	unknown	The suite reports this computation; the kernels and their outputs are not supplied in this round.

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
`4`	PDF p.167 (bytes of record)	suite text p.167: F4 group label
`24`	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)	LIB2-019 Route A selects the positive golden spectrum under its stated hypotheses	—
`related_to` (never evidential)	LIB2-020 Route B selects the positive golden-unit triple under DET-7	—
`cited_by_section`	E-C04.1.claims-used (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0050
`cited_by_section`	E-C04.1.derivation (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0060
`cited_by_section`	E-C04.1.prior-art (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0056
`cited_by_section`	E-C04.1.sources-receipt (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0065

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 (2)
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	s978 s981
candidate ids (frozen list S304)	C2-102

Drafting-lane note

Source-backed orbit obstruction associated with C2-102, not a second version of its spectral-selector theorem. The printed F4 notation is retained without an inferred real-form label.

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 5fc660466ebc218e3384ff92c10c25f4567bc762fc17006b022a47a13e7243ad

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-041 | 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