{
 "id": "LIB2-091",
 "entry_version": 8,
 "class": "CLAIM",
 "title": "The declared invariant-connection class cannot cancel the holonomy obstruction",
 "statement": "Within the declared left-E7(7)-invariant principal SU(8) connection class, the forced canonical connection has full SU(8) holonomy escaping Ksel, so no connection in that class cancels the obstruction.",
 "scope": {
  "carrier": "Principal SU(8) connections on the registered symmetric-space carrier",
  "domain": "The holonomy obstruction, not a topological nonexistence of all reductions or connections.",
  "group": "Left E7(7) invariance; principal SU(8)",
  "hypotheses": [
   "Use the declared invariant-connection class compatible with Ω and the loaded Ksel.",
   "The source’s Schur/Wang step leaves only the canonical symmetric-space connection."
  ],
  "physical_target": null,
  "quantifier": "Only the declared invariant-connection class.",
  "real_form": "E7(7)/SU(8)"
 },
 "source_labels_as_printed": {
  "math_status": "NOT_PRINTED",
  "attachment": "NOT_PRINTED",
  "scorecard_tier_word": null,
  "pdf_page": 183
 },
 "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 F",
  "section": "§8, Declared connection class",
  "pdf_page": 189,
  "quote": "left-E7(7) -invariant principal SU (8) connections compatible with Ω and the loaded Ksel ."
 },
 "caution": "This class-relative obstruction is not a topological no-section theorem and does not exclude a non-equivariant preserving connection.",
 "candidate_ids": [
  "C2-105"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "type": "related_to",
   "target": "LIB2-021"
  },
  {
   "type": "related_to",
   "target": "LIB2-045"
  }
 ],
 "url": "/library-v2/LIB2-091/",
 "content_sha256": "05b6eedb6981f7f463162b3fe1bfa6152878cbe6c8d3ebd84757d37d85ec09fa",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}