{
 "id": "LIB2-026",
 "entry_version": 11,
 "class": "CLAIM",
 "title": "A rank-character action represents the selector Hessian",
 "statement": "The registered rank-normalized carrier-character action Fchar has a critical point at the base with ∇²Fchar(I) = QT, and its displayed coefficients are traced to carrier ranks.",
 "scope": {
  "carrier": "Loaded plane PB, Frobenius-orthonormal p-basis and joint-defect projectors",
  "domain": "The displayed action and its second variation, not a uniqueness theorem for actions.",
  "group": null,
  "hypotheses": [
   "PB = iB iBᵀ is the loaded plane.",
   "The projectors Π1,Π32,Π36 and Ξ = Π10 − Π26 are the registered joint-defect projectors.",
   "Fchar is the particular nonlinear functional printed in Theorem 9.1."
  ],
  "physical_target": null,
  "quantifier": "The declared class only.",
  "real_form": "Frozen split-real carrier"
 },
 "source_labels_as_printed": {
  "math_status": "Certified",
  "attachment": "NOT_PRINTED",
  "scorecard_tier_word": null,
  "pdf_page": 296
 },
 "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 S",
  "section": "§9.1, Theorem 9.1: critical point and Hessian",
  "pdf_page": 313,
  "quote": "has its critical point at the base with ∇2 Fchar (I) = QT exactly"
 },
 "caution": "A variational representation of QT does not supply a microscopic principle selecting Fchar or its nonlinear shape.",
 "candidate_ids": [
  "C2-107"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "type": "depends_on",
   "target": "LIB2-025"
  },
  {
   "type": "cited_by_section",
   "target": "E-C04.2.claims-used"
  },
  {
   "type": "cited_by_section",
   "target": "E-C04.2.derivation"
  },
  {
   "type": "cited_by_section",
   "target": "E-C04.2.prior-art"
  },
  {
   "type": "cited_by_section",
   "target": "E-C04.2.sources-receipt"
  }
 ],
 "url": "/library-v2/LIB2-026/",
 "content_sha256": "d4dd4615a4746e327c4f299e50cebf956c386c6804e44bd3d92a636fa5579360",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}