{
 "id": "LIB2-171",
 "entry_version": 7,
 "class": "CLAIM",
 "title": "The pure MacDowell–Mansouri quadratic form is not a positive covariance",
 "statement": "On the registered 16-representation, BMM = tr(ΓTI TJ) has inertia (3,3,4), so the pure MM/EH weight cannot be a positive coercive covariance.",
 "scope": {
  "carrier": "The MacDowell–Mansouri quadratic form on the registered generator space",
  "domain": "The pure MM/EH quadratic form, distinct from the positive completion cone.",
  "group": null,
  "hypotheses": [
   "Use the registered 16-representation, generators and chirality trace."
  ],
  "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": "computational",
   "availability": "unknown"
  }
 ],
 "primary_source": {
  "component": "Appendix T",
  "section": "§7, Theorem 7.3: representation and quadratic form",
  "pdf_page": 322,
  "quote": "On the 16-representation, BC = −tr(TI TJ ) = 4I10 exactly, inertia (10, 0); BMM = tr(ΓTI TJ ) has characteristic polynomial"
 },
 "caution": "This finite-algebraic obstruction does not exclude the positive completion family or prove that a finite Cartan state is Einstein gravity.",
 "candidate_ids": [
  "C2-095"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "type": "related_to",
   "target": "LIB2-169"
  },
  {
   "type": "related_to",
   "target": "LIB2-170"
  }
 ],
 "url": "/library-v2/LIB2-171/",
 "content_sha256": "2313fcbd2ca764d9b3189c4415bac3c4a55b69620258cc98289d42853b6070f3",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}