Claims & Evidence Registrar › H02

LIB2-029 · The conditional selector for occupied golden mass-ladder rungs

Label sentence at the locator (PDF p.6 (bytes of record)):

Occupation selector → Derived-Conditional: three-layer derivation (mod-2/5/7), Appendix M.

Statement

The three-layer occupation selector has support O = {0,3,11,17} and period-two continuation {31,39}, conditional on the vacuum-to-projector bridge and the banked central sign T² = −I.

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 three-layer occupation selector has support O = {0,3,11,17} (one claim)
• p2 · period-two continuation {31,39} (one claim)

Scope

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.

Paper 0, Executive State Map: occupation-selector row — PDF p.6 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → CONTEXT · the lanes disagreed; resolved by PI ruling R80 as CONTEXT — R80 (S327): the principal investigator ruled the four disputed readings of read round 2 (D1289/D1290); a use resolved by ruling never anchors PUBLISHED

Occupation selector → Derived-Conditional: three-layer derivation (mod-2/5/7), Appendix M.

Appendix M, §7, Superseded note: selector support — PDF p.260 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS · the lanes agreed; the pattern ruled at R74/R80 re-opened it, set by PI ruling R82 as CONTEXT — R82 (S327): the principal investigator re-checked earlier categorizations against R78-a, R80 and R81 and re-opened two agreed readings; a use resolved by ruling never anchors PUBLISHED

construct a target-independent selector whose support is exactly O = {0, 3, 11, 17}

Appendix M, §7, Current conditional grade — PDF p.260 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → CONTEXT

That demand has now been met at derivation (not theorem-chain- complete) grade by the S224–S225 arc, and the occupation is promoted to Derived-Conditional.

Appendix M, §7, Live continuation — PDF p.260 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS

The derived selector’s period-two continuation is {31, 39},

Appendix M, §7, Conditional premises — PDF p.260 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS

Conditional on: the vacuum-to-projector bridge (§5 fences, carried verbatim) and the banked T 2 = −I.

Appendix M, §5, Vacuum-to-projector bridge fence — PDF p.259 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → SUPPORTS · the lanes disagreed; resolved by PI ruling R80 as CONTEXT — R80 (S327): the principal investigator ruled the four disputed readings of read round 2 (D1289/D1290); a use resolved by ruling never anchors PUBLISHED

The order-five realization is conditional on the vacuum-to- projector bridge Jvac 7→ v0 7→ p0 of the golden-Peirce construction, which is a naturalness claim, not proven canonical.

Evidence (availability is not outcome)

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.

Typed links

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

Machine certificate (R68)

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

Drafting-lane note

The imported Structural/Loaded-correspondence label is not propagated. The State Map explicitly prints Derived-Conditional; scorecard_tier_word uses the contract's case spelling. Its failure condition reverts occupation to Input if an established rung lies outside support or the testable continuation fails.

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 6135160202a5ec7f768c6c892f7ad47974df2dd3b37e7cb7123cd8e87885e600

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-029 | 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