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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-ca1454eef2561e4c3a8c67bc · master 6d82da907c52e8e6 · S329.

LIB2-084 · The mirror ladder reproduces an NS/R parity pattern, not a spin structure

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.269 (bytes of record)):

The signed trace over the banked mirror (Lucas ±) ladder reproduces the antiperiodic (NS) / periodic (R) parity pattern of the three-torus sector TS3 , with the Freudenthal bit playing the role of the holonomy sign.

Statement

The signed trace over the banked mirror/Lucas ladder reproduces the antiperiodic NS and periodic R parity pattern of the three-torus sector, with the Freudenthal bit playing the holonomy-sign role.

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 · The signed trace over the banked mirror/Lucas ladder reproduces the antiperiodic NS and periodic R parity pattern of the three-torus sector (one claim)
p2 · with the Freudenthal bit playing the holonomy-sign role. (one claim)

Scope

carrier	The banked mirror/Lucas ladder and TS3 sector
domain	The parity pattern only, without a manifold, Spin bundle or physical holonomy construction.
hypotheses	Use the registered signed trace, mirror ladder and Freudenthal bit.
quantifier	The two levels of the banked finite-carrier check.

What this does not show. The parity pattern does not construct a spin structure, a principal Spin bundle or a lift of a frame bundle.

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 P, §2, Theorem 2.3: signed-trace pattern — PDF p.284 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS

The signed trace over the banked mirror (Lucas ±) ladder reproduces the antiperiodic (NS) / periodic (R) parity pattern of the three-torus sector TS3 , with the Freudenthal bit playing the role of the holonomy sign.

The text extraction above lost mathematical typography. Restored from the sealed TeX source (rev32.7/tex/appendix_p_fifth_direction.tex:92-94): The signed trace over the banked mirror (Lucas ±) ladder reproduces the antiperiodic (NS) / periodic (R) parity pattern of the three-torus sector T³_S, with the Freudenthal bit playing the role of the holonomy sign. (R87 house restoration: rendered from the tex, not the quote; the quote above is what the machine gate matched)

Appendix P, §2, Theorem 2.3: binding F03 fence — PDF p.284 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: grok read THE_RECORD → CONTEXT · gemini read SUITE_TEXT_EXTRACT → CONTEXT

what is exhibited is the parity pattern a spin structure would produce, not a spin structure. No Spin-bundle map is constructed

Evidence (availability is not outcome)

kind	reference	line / key	availability	note
computational	s734, Appendix P §2, Theorem 2.3, p.269	—	unknown	The suite reports exact finite-data checks; the kernel and its output are not supplied in this round.

Typed links

type	target	licensed by
`related_to` (never evidential)	LIB2-054 The finite tick has an additive mirror-reversing grading	—
`cited_by_section`	E-C05.2.claims-used (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0191
`cited_by_section`	E-C05.2.prior-art (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0201
`cited_by_section`	E-C05.2.sources-receipt (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0212

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
Track-2 claim ids	A-5D-NS — cross-reference; the Track 1 / Track 2 join sets each one against what the sealed suite prints for this record. Where they differ, the suite is the record.
serials	s734
candidate ids (frozen list S304)	C2-027

Drafting-lane note

C2-027’s spin-structure shorthand is narrowed to the current parity-pattern statement, as required by the Rev29 F03 fence. The local theorem heading is not a scorecard tier. This is not the separately unlocated Track-2 parity lemma.

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 1b546a35f70d5947c5925560f5873506e8c8621457238f6623ddd3d9e5c63f75

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-084 | 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