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 4 of 4 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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-bace38ca9f1e7ce136a0c12a · master 0b0b838e8c4d1bc5 · S328.

LIB2-056 · The selected winding symmetry model has one scale class

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)):

one H 2 class in the selected symmetry model, whose census has ncyl = 2.

Statement

For the banked Sym(Wind) census with ncyl = 2, the scale-class count is dim H²(Sym;R+) = 1, with the area cocycle as generator.

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 the banked Sym(Wind) census with ncyl = 2, the scale-class count is dim H²(Sym;R+) = 1 (one claim)
p2 · with the area cocycle as generator. (one claim)

Scope

carrier	The banked winding symmetry census and its area cocycle
domain	One cohomology class in the selected symmetry model, not an exhaustive physical input census.
group	Sym(Wind) as registered
hypotheses	Use the banked Sym(Wind) identification and its two-cylinder census.
quantifier	The registered construction only.

What this does not show. The count does not establish exhaustiveness of the symmetry model or determine the numerical value of the physical scale.

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 2.4: census and cocycle — PDF p.285 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS

banked symmetry census (ncyl = 2): the generator is the area cocycle; the physical (both-flip) mirror preserves the class;

Appendix P, §2, Theorem 2.4: one class in the selected model — PDF p.285 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS

one H 2 class in the selected symmetry model, whose census has ncyl = 2.

The text extraction above lost mathematical typography. Restored from the sealed TeX source (rev32.7/tex/appendix_p_fifth_direction.tex:111-112): one H² class in the selected symmetry model, whose census has n_cyl=2. (R87 house restoration: rendered from the tex, not the quote; the quote above is what the machine gate matched)

Appendix P, §2, Theorem 2.4: exhaustiveness boundary — PDF p.285 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → CONTEXT

The theorem computes dim H 2 given the Sym(Wind) census; it does not establish that two cylinders are the only possibility, and exhaustiveness is open.

The text extraction above lost mathematical typography. Restored from the sealed TeX source (rev32.7/tex/appendix_p_fifth_direction.tex:114-117): The theorem computes dim H² given the Sym(Wind) census; it does not establish that two cylinders are the only possibility, and exhaustiveness is open. (R87 house restoration: rendered from the tex, not the quote; the quote above is what the machine gate matched)

Appendix P, §2, Continuation of the scale-class fence — PDF p.285 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → CONTEXT

being unconditional within the identification is not the same as the identification being forced, and the causal “because” is not carried.

Evidence (availability is not outcome)

kind	reference	line / key	availability	note
computational	s741; A1355, Appendix P §2, Theorem 2.4, pp.269–270	—	unknown	The suite reports the banked-generator census; its kernel and output are not supplied here.

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.269 (bytes of record)	closed form: dim H2(Sym;R+) = 1 for ncyl = 2 in Theorem 2.4
`1`	PDF p.269 (bytes of record)	closed form: dim H2(Sym;R+) = 1 for ncyl = 2 in Theorem 2.4

Typed links

type	target	licensed by
`cited_by_section`	E-C05.2.claims-used (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0190
`cited_by_section`	E-C05.2.prior-art (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0200
`cited_by_section`	E-C05.2.sources-receipt (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0211

Why this record is PUBLISHED (R67, condition T-B)

states a predicate	yes
uses on the record · unblocked	4 · 4
uses any lane has read	4 of 4
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
Track-2 claim ids	A-5D-SCALE, D-SCL-COUNT, E-SCL-COUNT — 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	A1355 s741
candidate ids (frozen list S304)	C2-028 C2-069 C2-080

Drafting-lane note

C2-028, C2-069 and C2-080 are one scale-class subject, not three independent results. The causal 'one input because two cylinders' inference is explicitly not reinstated; operational anchors remain a separate record.

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 a8a7aef7838955ddcb4494ec2daa7377e6fdad4fad745d98ca191ef69d98492f

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-056 | 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