{
 "id": "LIB2-088",
 "entry_version": 9,
 "class": "CLAIM",
 "title": "Generic cross-block Yukawa loops are not yet covered by an Artin generator census",
 "statement": "Artin’s theorem establishes associativity when a diagram’s internal labels lie in a two-generated subalgebra; that containment is not established for generic cross-block Yukawa trilinears with three independent split-octonion entries.",
 "scope": {
  "carrier": "Internal algebra labels in generic cross-block Yukawa diagrams",
  "domain": "The internal-label containment question; external momentum conservation does not settle it.",
  "group": null,
  "hypotheses": [
   "The ambient algebra is alternative.",
   "Artin’s conclusion applies where the diagram’s labels lie in a subalgebra generated by two elements."
  ],
  "physical_target": null,
  "quantifier": "The source-stated two-generator condition, not an unrestricted claim about all diagrams.",
  "real_form": "Split octonions Os"
 },
 "source_labels_as_printed": {
  "math_status": "NOT_PRINTED",
  "attachment": "NOT_PRINTED",
  "scorecard_tier_word": null,
  "pdf_page": 147
 },
 "house_tier": null,
 "review_state": "PUBLISHED",
 "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)",
 "evidence_status": [
  {
   "kind": "registry",
   "availability": "shipped"
  }
 ],
 "primary_source": {
  "component": "Appendix A",
  "section": "§A.7.8(ii), Conditional Artin application",
  "pdf_page": 153,
  "quote": "Where a diagram’s internal algebra labels lie in a subalgebra generated by two elements, associativity follows by Artin;"
 },
 "caution": "Lack of established two-generator containment is not a proof that a particular loop correction is non-associative or nonzero.",
 "candidate_ids": [
  "C2-114"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [],
 "url": "/library-v2/LIB2-088/",
 "content_sha256": "548f99fae7157b44f8e55dd8d9d8a9dc7f83bc9e6d227d44f0f7fdc21c310116",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}