{
 "id": "LIB2-015",
 "entry_version": 8,
 "class": "CLAIM",
 "title": "The golden braid-word square root on the frozen carrier",
 "statement": "In the frozen 56-frame, the braid hyperbolic word Wh has an exact symplectic unimodular square root Hϕ with Hϕ² = Wh and eigenvalues φ⁻¹, 1 and φ of multiplicities 12, 32 and 12.",
 "scope": {
  "carrier": "Frozen real 56-frame and its braid hyperbolic word",
  "domain": "Appendix H §11, the algebraic square-root construction.",
  "group": "Sp(V56)",
  "hypotheses": [
   "Wh, P, Q and the Clifford generators are those of the frozen representation.",
   "The source sets A = Wh − Q with A² − 3A + P = 0."
  ],
  "physical_target": null,
  "quantifier": "The specified braid word in the frozen frame.",
  "real_form": "Real symplectic carrier"
 },
 "source_labels_as_printed": {
  "math_status": "NOT_PRINTED",
  "attachment": "NOT_PRINTED",
  "scorecard_tier_word": null,
  "pdf_page": 198
 },
 "house_tier": null,
 "review_state": "PUBLISHED",
 "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)",
 "evidence_status": [
  {
   "kind": "computational",
   "availability": "unknown"
  }
 ],
 "primary_source": {
  "component": "Appendix H",
  "section": "§11, Theorem 11.1: frozen-word setup",
  "pdf_page": 205,
  "quote": "Within the frozen 56-frame let Wh = Q + 32 P + 32 γ1 − γ2 be the braid hyperbolic word and set A = Wh − Q, so that A2 − 3A + P = 0."
 },
 "caution": "This finite spectral construction does not attach the braid word to a physical mass, an absolute energy scale or an occupied winding level.",
 "candidate_ids": [
  "C2-104"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "type": "related_to",
   "target": "LIB2-014"
  },
  {
   "type": "cited_by_section",
   "target": "E-C05.2.claims-used"
  },
  {
   "type": "cited_by_section",
   "target": "E-C05.2.prior-art"
  },
  {
   "type": "cited_by_section",
   "target": "E-C05.2.sources-receipt"
  }
 ],
 "url": "/library-v2/LIB2-015/",
 "content_sha256": "db97b610554c7278b97a6640cd097c96b114a1b5b40b2924592c8a33d85ce8aa",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}