{
 "id": "LIB2-042",
 "entry_version": 9,
 "class": "CLAIM",
 "title": "A norm-only action leaves the regular norm-level directions flat",
 "statement": "For a twice-differentiable norm-only action S = F(α,N(X)), ambient stationarity in X at a regular norm-one point forces Hess S to vanish on ker dN, leaving at least 26 flats.",
 "scope": {
  "carrier": "Regular norm-level tangent directions in the stated cubic carrier",
  "domain": "The norm-only action subclass, not general invariant or source-dependent actions.",
  "group": null,
  "hypotheses": [
   "S depends on X only through N(X), with the other argument α fixed.",
   "The point is stationary, regular and norm-one."
  ],
  "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": 167
 },
 "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 E",
  "section": "§6(vi), Norm-only Hessian obstruction",
  "pdf_page": 174,
  "quote": "for any C 2 action S = F (α, N (X)), ambient stationarity in X at a regular norm-one point forces FN = 0 and hence Hess S ≡ 0 on ker dN , giving at least 26 flats structurally."
 },
 "caution": "The source check is on a generic symmetric cubic, not a dedicated full-Jordan computation, and the conclusion is limited to norm-only actions.",
 "candidate_ids": [
  "C2-102"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "type": "related_to",
   "target": "LIB2-041"
  },
  {
   "type": "cited_by_section",
   "target": "E-C04.1.claims-used"
  },
  {
   "type": "cited_by_section",
   "target": "E-C04.1.prior-art"
  },
  {
   "type": "cited_by_section",
   "target": "E-C04.1.sources-receipt"
  }
 ],
 "url": "/library-v2/LIB2-042/",
 "content_sha256": "0d50f5d03f3ab8dd4ec4e8ce1a2c210b81cf23aff57ce42a38b9a93816e4408a",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}