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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-2281b41679da88ed00195f88 · master ac37c14788254b3d · S327.

LIB2-039 · A fixed-grade cubic/current law cannot detect both dark directions

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)):

The fixed-grade cubic/current class is closed negative for rank-two detection (s1005–s1006).

Statement

In the declared fixed-grade cubic/current class, restriction to grade +2 gives rank 1 for Z ↦ P27 Z P27, so it cannot provide rank-two detection of the registered dark fibre.

Scope

carrier	The dark fibre restricted to the fixed +2 grade
domain	Rank-two detection inside a fixed grade; the embedding-tensor class was not decided.
hypotheses	The detector stays inside the fixed grade and uses the declared cubic/current class.; Both registered dark directions are required for rank-two detection.
quantifier	The declared class only.

What this does not show. This fixed-grade exclusion is not an embedding-tensor no-go; that separate class was scoped out for lack of a convention-certified branching artifact.

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(iv), Fixed-grade detection obstruction — PDF p.173 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS

The fixed-grade cubic/current class is closed negative for rank-two detection (s1005–s1006).

Appendix E, §6(iv), Rank witness — PDF p.173 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS

Restricting the dark fibre to the fixed +2 grade, rank (z2 ∋ Z 7→ P27 ZP27 ) = 1: one of the two dark directions moves the carrier out of the fixed grade entirely, with P27 ZP27 = 0 while [D56 , Z] ̸= 0,

Appendix E, §6(iv), Excluded scope — PDF p.173 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → CONTEXT

The embedding-tensor class is scoped out rather than decided, because no convention-certified branching artifact for it was supplied.

Evidence (availability is not outcome)

kind	reference	line / key	availability	note
computational	s1005–s1006, Appendix E §6(iv), 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
`+2`	PDF p.167 (bytes of record)	suite text p.167 only (no kernel line found)
`1`	PDF p.167 (bytes of record)	suite text p.167 only (no kernel line found)
`27`	PDF p.167 (bytes of record)	suite text p.167: P27 projector label

Typed links

type	target	licensed by
`related_to` (never evidential)	LIB2-036 An action depending only on the registered Gram map cannot select a coset point	—
`cited_by_section`	E-C04.2.claims-used (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0085
`cited_by_section`	E-C04.2.derivation (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0109, CIT-0132
`cited_by_section`	E-C04.2.sources-receipt (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0155

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 (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 T4-03, associated with the nearest selector-closure candidate C2-105. No conclusion is drawn about full-carrier detection.

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 2a70a1aa8b3bc411025169b35c38b30059e7baaacd0d85ab6a12e8b845fba4fa

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-039 | 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