{
 "id": "LIB2-021",
 "entry_version": 11,
 "class": "CLAIM",
 "title": "The finite loaded-profile parent action has its stated stable minimum",
 "statement": "Within the frozen split-real 56-frame and declared finite/internal loaded-profile class, Vtotal attains its stated global minimum at M* = I and the displayed source-aligned pair (j*,q*), with combined Hessian positive for every ρ,u0,κd > 0 on the directions transverse to the exact projective soft ray [W0] at zero inserted dark amplitude, along which it vanishes.",
 "scope": {
  "carrier": "Finite/internal loaded-profile selector in the frozen real V56",
  "domain": "Configuration-space minimum and stability, not the velocity Hessian used in the Legendre step.",
  "group": null,
  "hypotheses": [
   "The loaded boundary datum and assembled selector action are supplied.",
   "ρ,u0,κd are positive; no numerical values are fixed."
  ],
  "physical_target": null,
  "quantifier": "All positive parameters in the declared class.",
  "real_form": "Split-real 56-frame"
 },
 "source_labels_as_printed": {
  "math_status": "NOT_PRINTED",
  "attachment": "NOT_PRINTED",
  "scorecard_tier_word": null,
  "pdf_page": 170
 },
 "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": "§7, Closure declaration: minimum and Hessian",
  "pdf_page": 177,
  "quote": "the selector parent action Vtotal has its global minimum at (j ∗ , q ∗ = 32 j ∗ , M ∗ = I) with combined Hessian positive for all ρ, u0 , κd > 0 on the directions transverse to [W0 ], the exact projective soft ray at zero inserted dark amplitude, along which it vanishes (scope stated Rev32.9, A1632)."
 },
 "caution": "This finite configuration-space closure is not a continuum Hamiltonian or an interacting pole/LSZ construction.",
 "candidate_ids": [
  "C2-105"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "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"
  },
  {
   "type": "rests_on_premise",
   "target": "PRM-010"
  }
 ],
 "url": "/library-v2/LIB2-021/",
 "content_sha256": "ded57726ab8a0d82c2cb7e4449fb531e4f1726d205f11f1630594cf9e382dff9",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}