{
 "id": "LIB2-047",
 "entry_version": 7,
 "class": "CLAIM",
 "title": "The working golden vacuum has unit Jordan determinant",
 "statement": "At the working vacuum Jvac = diag(ϕ,1,ϕ⁻¹), the Jordan determinant is det Jvac = 1.",
 "scope": {
  "carrier": "The diagonal golden Jordan vacuum",
  "domain": "The determinant identity, not a new vacuum-selection law.",
  "group": null,
  "hypotheses": [
   "Use the working vacuum diag(ϕ,1,ϕ⁻¹) and the Jordan determinant."
  ],
  "physical_target": null,
  "quantifier": "The registered construction only.",
  "real_form": "J3(Os)"
 },
 "source_labels_as_printed": {
  "math_status": "NOT_PRINTED",
  "attachment": "NOT_PRINTED",
  "scorecard_tier_word": null,
  "pdf_page": 25
 },
 "house_tier": null,
 "review_state": "PUBLISHED",
 "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)",
 "evidence_status": [
  {
   "kind": "analytic",
   "availability": "shipped"
  }
 ],
 "primary_source": {
  "component": "Paper 1",
  "section": "§3, Roman-surface paragraph: vacuum adjoint",
  "pdf_page": 26,
  "quote": "The vacuum Jvac = diag(ϕ, 1, ϕ−1 ) satisfies Jvac # = diag(ϕ−1 , 1, ϕ) = J −1 (Jordan inverse), consistent vac with det Jvac = 1."
 },
 "caution": "Unit determinant alone does not select the golden spectrum; Appendix E uses it as a normalization hypothesis.",
 "candidate_ids": [
  "C2-002"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "type": "cited_by_section",
   "target": "E-C02.2.claims-used"
  },
  {
   "type": "cited_by_section",
   "target": "E-C02.2.derivation"
  },
  {
   "type": "cited_by_section",
   "target": "E-C02.2.prior-art"
  },
  {
   "type": "cited_by_section",
   "target": "E-C05.1.prior-art"
  }
 ],
 "url": "/library-v2/LIB2-047/",
 "content_sha256": "f1f16ca6fbecd42f4d9829f442101dc75965ec9e03ece4928375d4f7d42af1aa",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}