# LIB2-020 — Route B selects the positive golden-unit triple under DET-7

- 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 algebraic integers a,b,c in Q(√5) with abc = 1 and DET-7, Jvac = diag(a,b,c) has spectrum {ϕ,1,ϕ⁻¹} up to permutation.

## Caution

The arithmetic hypothesis and DET-7 remain premises; this result is not a derivation of the ordered physical frame or of an action.

## Primary source

Appendix E, §4, Theorem 2: arithmetic selector, PDF p.171: "Let Jvac = diag(a, b, c) with a, b, c > 0 algebraic integers in Q( 5) and abc = 1. Then (H2) forces Jvac = diag(ϕ, 1, ϕ−1 ) up to permuta- tion."

## Machine

- url: /library-v2/LIB2-020/
- content_sha256: 51dc78f16e2db545cbbde6fa79ec04f645ed89f162006264ab1bd6c608be7915
- candidate_ids: C2-102

## Freshness

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