{
 "id": "LIB2-041",
 "entry_version": 12,
 "class": "CLAIM",
 "title": "A frame-free invariant does not select the ordered Peirce frame",
 "statement": "A frame-free F4-invariant can at best select the spectral orbit of Jvac, not its ordered frame; at a stationary point on the registered orbit it has at least 24 Hessian zero modes.",
 "scope": {
  "carrier": "The ordered triple and its automorphism orbit",
  "domain": "Ordered-frame selection in the declared invariant class.",
  "group": "F4 automorphism action as printed",
  "hypotheses": [
   "The scalar is invariant under the frame-free F4 automorphism action as printed.",
   "The source identifies a 24-dimensional orbit of the ordered triple."
  ],
  "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"
  },
  {
   "kind": "computational",
   "availability": "unknown"
  }
 ],
 "primary_source": {
  "component": "Appendix E",
  "section": "§6(vi), Frame-free orbit obstruction",
  "pdf_page": 174,
  "quote": "a frame-free F4 -invariant can at best select the spectral orbit [Jvac ]F4 ; it can never isolate the ordered frame diag(φ, 1, φ−1 )."
 },
 "caution": "Selecting an ordered frame requires a loading or symmetry-breaking tensor; this result does not exclude selection with that additional datum.",
 "candidate_ids": [
  "C2-102"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "type": "related_to",
   "target": "LIB2-019"
  },
  {
   "type": "related_to",
   "target": "LIB2-020"
  },
  {
   "type": "cited_by_section",
   "target": "E-C04.1.claims-used"
  },
  {
   "type": "cited_by_section",
   "target": "E-C04.1.derivation"
  },
  {
   "type": "cited_by_section",
   "target": "E-C04.1.prior-art"
  },
  {
   "type": "cited_by_section",
   "target": "E-C04.1.sources-receipt"
  }
 ],
 "url": "/library-v2/LIB2-041/",
 "content_sha256": "5fc660466ebc218e3384ff92c10c25f4567bc762fc17006b022a47a13e7243ad",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}