{
 "id": "LIB2-019",
 "entry_version": 7,
 "class": "CLAIM",
 "title": "Route A selects the positive golden spectrum under its stated hypotheses",
 "statement": "A positive real diagonal Jvac satisfying unit determinant, inversion symmetry and DET-7 has spectrum {ϕ,1,ϕ⁻¹}, unique up to permutation.",
 "scope": {
  "carrier": "Positive real diagonal Jvac in J3(Os)",
  "domain": "Appendix E Route A; no number-field restriction is used.",
  "group": null,
  "hypotheses": [
   "H0: Det(Jvac) = 1.",
   "H1: Jvac is isospectral to its Jordan adjoint; at unit determinant this is inversion symmetry.",
   "H2: det Gram(Jvac,Jvac#) = 7."
  ],
  "physical_target": null,
  "quantifier": "Every positive real diagonal element satisfying H0–H2.",
  "real_form": "J3(Os)"
 },
 "source_labels_as_printed": {
  "math_status": "NOT_PRINTED",
  "attachment": "NOT_PRINTED",
  "scorecard_tier_word": null,
  "pdf_page": 164
 },
 "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": "§3, Theorem 1: symmetry-form selector",
  "pdf_page": 170,
  "quote": "A real positive diagonal Jvac ∈ J3 (Os ) satisfying (H0)–(H2) is unique up to permutation:"
 },
 "caution": "The theorem selects a spectral orbit only; it neither derives DET-7 nor selects an ordered physical Peirce frame.",
 "candidate_ids": [
  "C2-102"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
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 "url": "/library-v2/LIB2-019/",
 "content_sha256": "45087f33b267c3a0bf1f5263a6eb47481f9a1a405f3e2d8656d3eeb52b15a560",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}