{
 "id": "LIB2-020",
 "entry_version": 9,
 "class": "CLAIM",
 "title": "Route B selects the positive golden-unit triple under DET-7",
 "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.",
 "scope": {
  "carrier": "Positive diagonal Jvac = diag(a,b,c)",
  "domain": "Appendix E Route B with the replaced admissible-gap proof.",
  "group": null,
  "hypotheses": [
   "a,b,c are positive algebraic integers in Q(√5).",
   "abc = 1, so the entries are units of Z[ϕ].",
   "H2: det Gram(Jvac,Jvac#) = 7."
  ],
  "physical_target": null,
  "quantifier": "Every triple satisfying the printed arithmetic hypotheses.",
  "real_form": "J3(Os)"
 },
 "source_labels_as_printed": {
  "math_status": "NOT_PRINTED",
  "attachment": "NOT_PRINTED",
  "scorecard_tier_word": null,
  "pdf_page": 165
 },
 "house_tier": null,
 "review_state": "PUBLISHED",
 "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)",
 "evidence_status": [
  {
   "kind": "analytic",
   "availability": "shipped"
  }
 ],
 "primary_source": {
  "component": "Appendix E",
  "section": "§4, Theorem 2: arithmetic selector",
  "pdf_page": 171,
  "quote": "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."
 },
 "caution": "The arithmetic hypothesis and DET-7 remain premises; this result is not a derivation of the ordered physical frame or of an action.",
 "candidate_ids": [
  "C2-102"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "type": "uses_input",
   "target": "LIB2-018"
  },
  {
   "type": "rests_on_premise",
   "target": "PRM-013"
  },
  {
   "type": "rests_on_premise",
   "target": "PRM-024"
  },
  {
   "type": "cited_by_section",
   "target": "E-C04.1.claims-used"
  },
  {
   "type": "cited_by_section",
   "target": "E-C04.1.derivation"
  },
  {
   "type": "cited_by_section",
   "target": "E-C04.1.prior-art"
  },
  {
   "type": "cited_by_section",
   "target": "E-C04.1.sources-receipt"
  }
 ],
 "url": "/library-v2/LIB2-020/",
 "content_sha256": "51dc78f16e2db545cbbde6fa79ec04f645ed89f162006264ab1bd6c608be7915",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}