{
 "id": "LIB2-036",
 "entry_version": 7,
 "class": "CLAIM",
 "title": "An action depending only on the registered Gram map cannot select a coset point",
 "statement": "No action factoring only through the registered Gram map GB can uniquely select a coset point, because its two-dimensional dark fibre is invisible to that map.",
 "scope": {
  "carrier": "GB(M) = iBᵀ M iB on the registered scalar coset",
  "domain": "The GB-factoring subclass at every order; wider parent actions and boundary laws are excluded from this claim.",
  "group": null,
  "hypotheses": [
   "The action factors only through GB.",
   "The registered map has the dark fibre reported in Appendix E §6(i)."
  ],
  "physical_target": null,
  "quantifier": "The declared class only.",
  "real_form": "E7(7)/SU(8)"
 },
 "source_labels_as_printed": {
  "math_status": "NOT_PRINTED",
  "attachment": "NOT_PRINTED",
  "scorecard_tier_word": null,
  "pdf_page": 166
 },
 "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 E",
  "section": "§6(i), Gram-only selector obstruction",
  "pdf_page": 172,
  "quote": "Consequently no action factoring only through GB can uniquely select a coset point — not obstructed at some order, but dead at every order."
 },
 "caution": "This exclusion does not apply to parent actions that use additional full-carrier or boundary information.",
 "candidate_ids": [
  "C2-105"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "type": "related_to",
   "target": "LIB2-021"
  },
  {
   "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"
  }
 ],
 "url": "/library-v2/LIB2-036/",
 "content_sha256": "909ab69958186f61db3b17438e4dbcd60c00a280fe99a1f2eba0d798bc24fc23",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}