{
 "id": "LIB2-189",
 "entry_version": 8,
 "class": "CLAIM",
 "title": "The anisotropic heat-kernel family has nonlinear OS positivity in its cone",
 "statement": "In the declared anisotropic heat-kernel family with α > |β|, the positive elliptic invariant generates a positive Markov convolution whose reflected-kernel factorization gives OS positivity.",
 "scope": {
  "carrier": "The anisotropic heat-kernel family generated by Lα,β",
  "domain": "Nonlinear reflection positivity in the declared heat-kernel family at regulator tier.",
  "group": null,
  "hypotheses": [
   "Use the registered invariant operator Lα,β and its coefficient cone α > |β|.",
   "Use the reflected-kernel factorization of Proposition 8.5."
  ],
  "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": 307
 },
 "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 T",
  "section": "§8, Proposition 8.5: nonlinear reflection positivity",
  "pdf_page": 324,
  "quote": "Lα,β is a positive elliptic invariant on the whole cone α > |β|, the heat semigroup is a positive Markov convolution, and the reflected-kernel factorization gives OS positivity."
 },
 "caution": "This family-specific reflection positivity does not establish a general gravitational measure or a continuum Einstein limit.",
 "candidate_ids": [
  "C2-094"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "type": "related_to",
   "target": "LIB2-170"
  },
  {
   "type": "related_to",
   "target": "LIB2-172"
  }
 ],
 "url": "/library-v2/LIB2-189/",
 "content_sha256": "f968f54fc4ff5d174e5127863e36a508991ef0abb0b91972aa76b48d82237996",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}