{
 "id": "LIB2-181",
 "entry_version": 8,
 "class": "CLAIM",
 "title": "The local covariant odd response is one orbit with an unselected torsor",
 "statement": "On the transported paired-shell space, HomS3(J−,sgn) has real dimension 4; its normalized sphere is one connected-covariance orbit, leaving the endpoint-exchange torsor τ = ±1 unselected.",
 "scope": {
  "carrier": "The transported paired-shell generation space and its odd source-character intertwiners",
  "domain": "The local response class at the transported point, not a selected microscopic readout.",
  "group": null,
  "hypotheses": [
   "Use the transported pointed carrier and the connected covariance-group equivalence.",
   "Normalize the source intertwiner without choosing an endpoint-exchange side."
  ],
  "physical_target": null,
  "quantifier": "The registered construction and its stated premises.",
  "real_form": null
 },
 "source_labels_as_printed": {
  "math_status": "NOT_PRINTED",
  "attachment": "NOT_PRINTED",
  "scorecard_tier_word": null,
  "pdf_page": 316
 },
 "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 T",
  "section": "§15.2, Source-intertwiner space and covariance orbit",
  "pdf_page": 334,
  "quote": "On the transported paired-shell generation space G6 , the source intertwiner space HomS3 (J− , sgn) has real dimension four, while its normalized sphere is a single orbit of the connected covariance group."
 },
 "caution": "A single equivalence class is not a selected representative, endpoint orientation or physical response coefficient.",
 "candidate_ids": [
  "C2-134"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "type": "related_to",
   "target": "LIB2-013"
  },
  {
   "type": "related_to",
   "target": "LIB2-179"
  },
  {
   "type": "related_to",
   "target": "LIB2-180"
  }
 ],
 "url": "/library-v2/LIB2-181/",
 "content_sha256": "5881646a8c47d2549361508da35526323da880c02d5f5bd1ccbf59bf5a6c354f",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}