{
 "id": "LIB2-105",
 "entry_version": 13,
 "class": "CLAIM",
 "title": "The stated split-G2 involution family yields no positive equivariant polarization",
 "statement": "In the declared split-G2 family, the four equivariant involutions J = sP1 + tPIm give signatures (4,4), (5,3), (3,5) and (4,4); none is positive.",
 "scope": {
  "carrier": "Equivariant polarizing involutions on the split-octonion carrier",
  "domain": "The enumerated equivariant involution family, not arbitrary polarizations or other real forms.",
  "group": "Der(Os)-equivariance",
  "hypotheses": [
   "The commutant of Der(Os) in End(Os) has the source-reported dimension two.",
   "The split norm on Im Os has signature (3,4).",
   "Use involutions of the stated form J = sP1 + tPIm; Appendix Q retains its κphys conditional tier."
  ],
  "physical_target": null,
  "quantifier": "The declared source class only.",
  "real_form": "Split G2 / split octonions"
 },
 "source_labels_as_printed": {
  "math_status": "NOT_PRINTED",
  "attachment": "NOT_PRINTED",
  "scorecard_tier_word": null,
  "pdf_page": 277
 },
 "house_tier": null,
 "review_state": "PUBLISHED",
 "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)",
 "evidence_status": [
  {
   "kind": "registry",
   "availability": "shipped"
  }
 ],
 "primary_source": {
  "component": "Appendix Q",
  "section": "§3(ii), Polarization obstruction",
  "pdf_page": 292,
  "quote": "No positive equivariant polarization exists in the split-G2 family."
 },
 "caution": "The exclusion is confined to the stated equivariant split-real involutions; it does not rule out polarizations using additional data.",
 "candidate_ids": [
  "C2-042"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "type": "related_to",
   "target": "LIB2-104"
  },
  {
   "type": "related_to",
   "target": "LIB2-096"
  },
  {
   "type": "rests_on_premise",
   "target": "PRM-002"
  }
 ],
 "url": "/library-v2/LIB2-105/",
 "content_sha256": "d9ecd47fc9bbcf6b5b912df6090000a2edbb2ec04650549f2c1e0e1e0a7cec52",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}