{
 "id": "LIB2-083",
 "entry_version": 7,
 "class": "CLAIM",
 "title": "The loaded local matter action has a correlated Z6 kernel",
 "statement": "On the loaded one-generation field dictionary, the correlated cyclic Z6 centre acts trivially on all sixteen states, yielding the faithful local action GSM/Z6.",
 "scope": {
  "carrier": "The sixteen-state one-generation field dictionary",
  "domain": "The trivially acting central subgroup, not the physical global bundle or line-operator choice.",
  "group": "GSM/Z6",
  "hypotheses": [
   "Use Q = T3 + Y and the registered colour-triality and weak-duality assignments.",
   "The source evaluates 6Y + 2t + 3d ≡ 0 mod 6 on the whole package."
  ],
  "physical_target": null,
  "quantifier": "The local action on the specified matter states.",
  "real_form": "Compact GSM action"
 },
 "source_labels_as_printed": {
  "math_status": "NOT_PRINTED",
  "attachment": "NOT_PRINTED",
  "scorecard_tier_word": null,
  "pdf_page": 178
 },
 "house_tier": null,
 "review_state": "PUBLISHED",
 "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)",
 "evidence_status": [
  {
   "kind": "analytic",
   "availability": "shipped"
  }
 ],
 "primary_source": {
  "component": "Appendix F",
  "section": "§4.1, State-by-state centre check",
  "pdf_page": 185,
  "quote": "All sixteen states satisfy (3), so g generates a Z6 = Z3 × Z2 that acts trivially on the whole package;"
 },
 "caution": "The faithful local quotient does not fix the physical global structure or the allowed line operators.",
 "candidate_ids": [
  "C2-043"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "type": "related_to",
   "target": "LIB2-081"
  }
 ],
 "url": "/library-v2/LIB2-083/",
 "content_sha256": "19f447d3c8b4a11ab1c3bfdb084dd16a8f35a3c9537a22eb9bbcd46a669136e2",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}