# LIB2-001 — Route-B admissible-gap classification

- class: CLAIM · review_state: PUBLISHED · house_tier: not yet assigned
- labels as printed: math_status NOT_PRINTED · attachment NOT_PRINTED · scorecard tier word none (PDF p.165)
- basis: {"pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369"}

## Statement

For positive golden-field units a, b, c with abc = 1, the Route-B classification gives F = 16 only at the exponent multiset {1, 0, −1}; apart from the equal-spectrum case, every other admissible gap pair has F ≥ 41.

## Caution

This gap classification does not select the golden-field hypothesis or the ordered physical Peirce frame, and it does not supply a physical vacuum-selection law.

## Primary source

Appendix E, §4, Theorem 2: admissible-gap case count, PDF p.171: "(p, q) = (1, 1) — the triple {1, 0, −1} — gives F = 3 + 3 + 3 + 7 = 16; no other pair with p + q ≤ 2 is admissible (p + 2q ≡ 0 (mod 3) excludes (1, 0), (0, 1), (2, 0), (0, 2)); for p + q = 3 the admissible pairs are (3, 0) and (0, 3), each giving F = 3 + 18 + 2 + 18 = 41 (attained at {2, −1, −1}); and for p + q ≥ 4, Ap+q ≥ 47 gives F ≥ 3 + 47 + 2 + 2 = 54"

## Machine

- url: /library-v2/LIB2-001/
- content_sha256: cb263cc9d60e7eefdc392d9a5e109dcfa3ee16aa24105056057b1226784566ac
- candidate_ids: C2-111

## Freshness

- BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02
- Declared volatile fields (R36): BUILD_STAMP