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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-fcd8fbba3c647a64ecbb57a3 · master 0b0b838e8c4d1bc5 · S328.

LIB2-054 · The finite tick has an additive mirror-reversing grading

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 Z4 clock weight of the banked grading behaves as a momentum-like quantum number modulo 4: the grading law, additivity under composition, and reversal under the mirror are all exact on the full generator set.

Statement

The banked clock weight is an exact Z4-valued grading, additive under composition and reversed by the mirror on the full registered generator set.

Parts of the statement (3)

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 banked clock weight is an exact Z4-valued grading (one claim)
p2 · additive under composition (one claim)
p3 · reversed by the mirror on the full registered generator set. (one claim)

Scope

carrier	The banked winding-category generators
domain	An internal grading, not a spacetime identification.
group	Z4 grading
hypotheses	Use the registered composition and mirror operations on the full generator set.
quantifier	The full registered generator set.

What this does not show. This grading is not a physical momentum conjugate to a constructed compact coordinate.

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 2.1: tick grading — PDF p.284 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS

The Z4 clock weight of the banked grading behaves as a momentum-like quantum number modulo 4: the grading law, additivity under composition, and reversal under the mirror are all exact on the full generator set.

Appendix P, §2, Theorem 2.1: compact-coordinate boundary — PDF p.284 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → CONTEXT

No compact-coordinate map is constructed — there is no internal x5 , no periodic identification, and no Fourier duality between the grading and any coordinate anywhere in the banked material.

The text extraction above lost mathematical typography. Restored from the sealed TeX source (rev32.7/tex/appendix_p_fifth_direction.tex:72-74): No compact-coordinate map is constructed — there is no internal x⁵, no periodic identification, and no Fourier duality between the grading and any coordinate anywhere in the banked material. (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	s740, Appendix P §2, Theorem 2.1, p.269	—	unknown	The suite reports the generator-set check; the kernel and its 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
`4`	PDF p.269 (bytes of record)	suite text p.269: Z4 grading and modulo-four law (no kernel line found)

Typed links

type	target	licensed by
`cited_by_section`	E-C05.2.claims-used (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0188
`cited_by_section`	E-C05.2.prior-art (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0198
`cited_by_section`	E-C05.2.sources-receipt (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0209

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-TICK — 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	s740
candidate ids (frozen list S304)	C2-029

Drafting-lane note

C2-029 retains the formal momentum-like properties only. No compact coordinate, periodic spacetime or Fourier-dual momentum is added; the local theorem heading is not a scorecard tier.

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 7c086a7c8178e69bdb1ca0c8b4313ba6907e02a39282aa9235ed36c3a474367c

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-054 | 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