{
 "id": "LIB2-078",
 "entry_version": 9,
 "class": "CLAIM",
 "title": "The frame-free real 56 has no invariant rank-one Higgs projector",
 "statement": "The bare real 56 admits no E7(7)-invariant rank-one projector; its invariant idempotents have ranks only 0 or 56.",
 "scope": {
  "carrier": "Real Freudenthal carrier F = R ⊕ R ⊕ J3(Os) ⊕ J3(Os)",
  "domain": "The unmarked real carrier, without a boundary selecting a line.",
  "group": "G0 = Aut(F,ω,Q)0",
  "hypotheses": [
   "The full frame-free E7(7) action is retained.",
   "The source computes its real commutant as R·I."
  ],
  "physical_target": null,
  "quantifier": "Every invariant idempotent for the registered full action.",
  "real_form": "E7(7)"
 },
 "source_labels_as_printed": {
  "math_status": "NOT_PRINTED",
  "attachment": "NOT_PRINTED",
  "scorecard_tier_word": null,
  "pdf_page": 182
 },
 "house_tier": null,
 "review_state": "PUBLISHED",
 "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)",
 "evidence_status": [
  {
   "kind": "analytic",
   "availability": "shipped"
  },
  {
   "kind": "computational",
   "availability": "unknown"
  }
 ],
 "primary_source": {
  "component": "Appendix F",
  "section": "§7, Theorem 7.1: invariant projectors",
  "pdf_page": 188,
  "quote": "There is no G0 -invariant rank-one projector on the 56: the only invariant idempotents have rank 0 or 56."
 },
 "caution": "The obstruction does not exclude a Higgs orientation supplied by a loaded boundary or selected by additional symmetry-breaking structure.",
 "candidate_ids": [
  "C2-041"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "type": "related_to",
   "target": "LIB2-006"
  }
 ],
 "url": "/library-v2/LIB2-078/",
 "content_sha256": "02a37a6ebb0556d14d97e0e4b160dfcdc735e1115e658118c5c49ddcf270823a",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}