{
 "id": "LIB2-161",
 "entry_version": 11,
 "class": "CLAIM",
 "title": "The registered up–down operation is a parity, not a derived isospin action",
 "statement": "The registered u ↔ d operation is the split-octonion sign map e7 → −e7, exchanging Hu and Hd as a Z2 parity rather than a derived SU(2) action.",
 "scope": {
  "carrier": "The split-octonion sign map e7 → −e7 on the loaded up/down Higgs dictionary",
  "domain": "The registered up–down operation, not a derived nuclear SU(2) dynamics.",
  "group": null,
  "hypotheses": [
   "Use the A689 field dictionary and its registered sign map (read literally, the flip of e7 alone; neither it nor full conjugation is a Jordan automorphism)."
  ],
  "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": 133
 },
 "house_tier": null,
 "review_state": "PUBLISHED",
 "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)",
 "evidence_status": [
  {
   "kind": "computational",
   "availability": "unknown"
  }
 ],
 "primary_source": {
  "component": "Paper 9",
  "section": "§9, Registered up–down operation",
  "pdf_page": 138,
  "quote": "The only registered u ↔ d object is the Os sign map e7 → −e7 (Hu ↔ Hd ; A689 dictionary; read literally, the flip of e7 alone — s1170 shows the phrase also fits full conjugation, and neither map is a Jordan automorphism) — a Z2 parity, not an SU (2)"
 },
 "caution": "The parity does not construct a continuous isospin action or supply the missing QCD flip energy.",
 "candidate_ids": [
  "C2-129"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "type": "related_to",
   "target": "LIB2-160"
  },
  {
   "type": "related_to",
   "target": "LIB2-108"
  }
 ],
 "url": "/library-v2/LIB2-161/",
 "content_sha256": "1da0dbf7e4438d88577deeb9f05db0ff19c0a064c9a29c7379060101bf1123ef",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}