{
 "id": "LIB2-180",
 "entry_version": 8,
 "class": "CLAIM",
 "title": "The transported A689 grading has trivial rather than alternating character",
 "statement": "The transported A689 split-norm Z2 grading carries the trivial, not alternating, S3 character, so its direct identification with Hsgn is closed negative.",
 "scope": {
  "carrier": "The transported multiplicative grading and the Hermitian sign-character line",
  "domain": "The direct grading-to-sign-line shortcut, not every possible odd response.",
  "group": null,
  "hypotheses": [
   "Use the registered A689 grading and its transported S3 action."
  ],
  "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, Grading character",
  "pdf_page": 334,
  "quote": "the A689 split-norm Z2 was computed to carry the trivial, not the alternating, S3 character [A1556]."
 },
 "caution": "This character mismatch does not eliminate covariant source-character intertwiners or select an endpoint orientation.",
 "candidate_ids": [
  "C2-134"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "type": "related_to",
   "target": "LIB2-179"
  }
 ],
 "url": "/library-v2/LIB2-180/",
 "content_sha256": "f6682a9f7eb0bd07e781c0ec7ec7ad488994ffc8d63b0689c8a5c82d2b720907",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}