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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-8cbbfa81813f28352b26b20c · master ac37c14788254b3d · S327.

LIB2-040 · An RB-even action cannot select the horizontal-orbit sign

class CLAIMmath status (as printed) NOT_PRINTEDattachment (as printed) NOT_PRINTEDscorecard tier word (as printed) none printedhouse tier not yet assignedreview state PUBLISHEDentry version 8

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

An RB -even action cannot resolve the sign — the parity of the law, not its strength, is what fails.

Statement

For X in the registered horizontal 16-dimensional sector, every RB-conjugation-invariant scalar obeys S(exp(2tX)) = S(exp(−2tX)), so an RB-even action cannot resolve that sign.

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 X in the registered horizontal 16-dimensional sector, every RB-conjugation-invariant scalar obeys S(exp(2tX)) = S(exp(−2tX)) (one claim)
p2 · an RB-even action cannot resolve that sign. (one claim)

Scope

carrier	The horizontal 16-dimensional sector and its exponential orbit
domain	The horizontal sign pair in the declared even-action class.
hypotheses	RB e^(2tX) RB = e^(-2tX) in the registered carrier.; S is invariant under RB conjugation.
quantifier	The declared class only.

What this does not show. This symmetry obstruction requires an RB-odd ingredient somewhere; it does not itself construct or select that ingredient.

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(v), Even-action sign obstruction — PDF p.173 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS

An RB -even action cannot resolve the sign — the parity of the law, not its strength, is what fails.

Appendix E, §6(v), Orbit relation and invariant scalar — PDF p.173 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS

For X in the horizontal 16-dimensional sector, RB e2tX RB = e−2tX (house-verified numerically), so every RB -conjugation-invariant scalar satisfies S(e2tX ) = S(e−2tX ).

The text extraction above lost mathematical typography. Restored from the sealed TeX source (rev32.7/tex/appendix_e_vacuum_selector.tex:222-224): For X in the horizontal 16-dimensional sector, R_(B)e^(2tX)R_B=e^(-2tX) (house-verified numerically), so every R_B-conjugation-invariant scalar satisfies S(e^(2tX))=S(e^(-2tX)) (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
computational	s1005–s1006, Appendix E §6(v), 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
`16`	PDF p.167 (bytes of record)	suite text p.167 only (no kernel line found)
`2`	PDF p.167 (bytes of record)	closed form: S(e2tX) = S(e−2tX) printed in §6(v)
`−2`	PDF p.167 (bytes of record)	closed form: S(e2tX) = S(e−2tX) printed in §6(v)

Typed links

type	target	licensed by
`cited_by_section`	E-C04.2.claims-used (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0086
`cited_by_section`	E-C04.2.derivation (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0110, CIT-0133
`cited_by_section`	E-C04.2.prior-art (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0100
`cited_by_section`	E-C04.2.sources-receipt (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0156

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	s1005 s1006
candidate ids (frozen list S304)	C2-105

Drafting-lane note

Source-backed missing proposal T4-04, associated with C2-105. It concerns the registered horizontal sign, not the PMNS atmospheric-octant registration.

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 f1b7528434a495572f8ab5326545f4ebecf65eb5891c196bb308676232cbe6c6

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-040 | 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