{
 "id": "LIB2-027",
 "entry_version": 7,
 "class": "CLAIM",
 "title": "The declared action-completion class retains nonlinear-shape freedom",
 "statement": "In the declared rank-normalized character-completion class, actions with a critical point at the base and positive-semidefinite Hessian form, modulo equivalence, a four-dimensional moduli space: three Hessian-weight ratios and one nonlinear modulus invisible to the complete two-jet.",
 "scope": {
  "carrier": "Nonlinear actions in the declared rank-normalized character-completion class",
  "domain": "The declared completion class before adopting Φdiag; not every possible action class.",
  "group": null,
  "hypotheses": [
   "Use the class and equivalence relation declared before the source analysis.",
   "Require a critical point at the base and positive-semidefinite Hessian."
  ],
  "physical_target": null,
  "quantifier": "The declared class only.",
  "real_form": null
 },
 "source_labels_as_printed": {
  "math_status": "NOT_PRINTED",
  "attachment": "NOT_PRINTED",
  "scorecard_tier_word": null,
  "pdf_page": 297
 },
 "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": "§9.4, Theorem 9.4: moduli space",
  "pdf_page": 314,
  "quote": "the solution set of “critical point at the base + positive-semidefinite Hessian” modulo equivalence is a four-dimensional moduli space,"
 },
 "caution": "This obstruction is class-relative; enlarging the class changes its moduli count, and matching a Hessian alone does not select an action.",
 "candidate_ids": [
  "C2-108"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "type": "related_to",
   "target": "LIB2-026"
  },
  {
   "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/LIB2-027/",
 "content_sha256": "5ba75a403cc9ab5f826fd19ca3c8bee4731163dc8bc8756398cc983b5a1c8fa5",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}