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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-808ddc2be76f9e04b39b1472 · master 6d82da907c52e8e6 · S329.

LIB2-085 · The finite signatures require an internal structure or its equivalent proxy

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.270 (bytes of record)):

A four-dimensional model that lacks the equivalent internal structure — a noncompact internal modulus, an internal H 1 (−; Z2 ) / w1 ̸= 0 twisted bundle, and an internal grading circle — cannot reproduce the three banked signatures

Statement

In the declared comparison class, bare four-dimensional spacetime data without the equivalent noncompact modulus, twisted internal bundle or grading variable cannot reproduce the three banked signatures.

Scope

carrier	The three banked finite-carrier signatures and the declared four-dimensional comparison class
domain	The structure-necessity argument of Appendix P, not a spacetime-dimension measurement.
hypotheses	No equivalent noncompact internal target modulus, twisted internal bundle or grading variable is supplied.
quantifier	The declared comparison class, not four-dimensional theories with additional internal data.

What this does not show. This argument does not force a fifth physical spacetime dimension; a four-dimensional model may import equivalent internal data.

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

A four-dimensional model that lacks the equivalent internal structure — a noncompact internal modulus, an internal H 1 (−; Z2 ) / w1 ̸= 0 twisted bundle, and an internal grading circle — cannot reproduce the three banked signatures

The text extraction above lost mathematical typography. Restored from the sealed TeX source (rev32.7/tex/appendix_p_fifth_direction.tex:122-124): A four-dimensional model that lacks the equivalent internal structure — a noncompact internal modulus, an internal H¹(-;ℤ₂) / w₁≠0 twisted bundle, and an internal grading circle — cannot reproduce the three banked signatures (R87 house restoration: rendered from the tex, not the quote; the quote above is what the machine gate matched)

Appendix P, §2, Remark 2.6: equivalent internal data — PDF p.285 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS

The claim is that the three signatures cannot arise from bare four-dimensional spacetime data with no such internal structure; they demand either a fifth direction or its internal proxy.

Evidence (availability is not outcome)

kind	reference	line / key	availability	note
registry	A1356, Appendix P §2, Theorem 2.5 and Remark 2.6, p.270	—	shipped	The source prints the comparison-class argument and its internal-proxy escape; the original hostile-lane return is not supplied here.

Typed links

type	target	licensed by
`related_to` (never evidential)	LIB2-055 The finite carrier fails the cylinder-condition count	—
`related_to` (never evidential)	LIB2-084 The mirror ladder reproduces an NS/R parity pattern, not a spin structure	—

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
Track-2 claim ids	A-5D-NEC — 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	A1356
candidate ids (frozen list S304)	C2-026

Drafting-lane note

C2-026 keeps the source’s domain-relative necessity statement. It is separate from the finite cylinder-condition count and from the interpretive Kaluza–Klein discussion that follows.

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 73d8562d18e2632d8f8863dff75e28ba7790650f9b4dc4ba87949c2978dc1c5d

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-085 | 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