{
 "id": "LIB2-170",
 "entry_version": 9,
 "class": "CLAIM",
 "title": "A reflection-positive Cartan state exists at finite regulator",
 "statement": "The registered heat-kernel × Haar product on Spin(5) edges gives a normalized reflection-positive state, an OS Hilbert space and a positive transfer operator at finite regulator.",
 "scope": {
  "carrier": "The finite Cartan regulator with a heat-kernel × Haar edge measure",
  "domain": "Finite-regulator state, OS Hilbert space and transfer operator only.",
  "group": "Spin(5)",
  "hypotheses": [
   "Use the registered compact Spin(5) edge measure, crossing split and nonnegative Peter–Weyl coefficients."
  ],
  "physical_target": null,
  "quantifier": "The registered construction and its stated premises.",
  "real_form": null
 },
 "source_labels_as_printed": {
  "math_status": "NOT_PRINTED",
  "attachment": "NOT_PRINTED",
  "scorecard_tier_word": null,
  "pdf_page": 305
 },
 "house_tier": null,
 "review_state": "PUBLISHED",
 "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)",
 "evidence_status": [
  {
   "kind": "registry",
   "availability": "shipped"
  },
  {
   "kind": "computational",
   "availability": "unknown"
  }
 ],
 "primary_source": {
  "component": "Appendix T",
  "section": "§7, Named datum 7.1: finite state",
  "pdf_page": 321,
  "quote": "A normalized reflection-positive state exists at the finite Cartan regulator tier: a heat-kernel × Haar product on Spin(5) edges,"
 },
 "caution": "Finite-regulator existence does not establish the continuum limit, Einstein universality or a selected coherent boundary state.",
 "candidate_ids": [
  "C2-094"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "type": "related_to",
   "target": "LIB2-169"
  },
  {
   "type": "rests_on_premise",
   "target": "PRM-014"
  }
 ],
 "url": "/library-v2/LIB2-170/",
 "content_sha256": "ac55344f3cc1cf8beb5682b46536fc148025bb9beec04402f6915b2d03206195",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}