{
 "id": "LIB2-113",
 "entry_version": 9,
 "class": "CLAIM",
 "title": "Reynolds preservation of the registered raw coefficient ray",
 "statement": "The loaded U(1)Y Reynolds average PY=0 is the identity on the span of the four displayed Yukawa channel tensors, each of total hypercharge 0, so it retains every coefficient vector on that span without reweighting — in particular the common ray (1,1,1,1) of the registered raw tensor. This is preservation, not selection: nothing in the projection excludes an unequal quartet on the same span.",
 "scope": {
  "carrier": "The span of the four displayed Yukawa channel tensors, all of total hypercharge 0 (s1171 T1)",
  "domain": "UV/matching coefficients, not low-energy equality.",
  "group": "U(1)Y (loaded hypercharge), acting trivially on the four-channel span; the multiplicity-one premise is exhibited on the model group S4 (Appendix K §3.3, p.234), not on this action",
  "hypotheses": [
   "None beyond total hypercharge 0 on the four displayed tensors: the retention statement needs no multiplicity-one and no channel-transitivity premise.",
   "Split G2(2) setting as registered; the §2.2 transitivity argument is NOT used (A1717-F02)."
  ],
  "physical_target": null,
  "quantifier": "Every coefficient vector on that span; the (1,1,1,1) ray is named as the instance the suite carries",
  "real_form": "Split G2(2) setting"
 },
 "source_labels_as_printed": {
  "math_status": "NOT_PRINTED",
  "attachment": "NOT_PRINTED",
  "scorecard_tier_word": null,
  "pdf_page": 230
 },
 "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 K",
  "section": "§3.3, Reynolds-forced equal weights",
  "pdf_page": 241,
  "quote": "(Rev32.9, A1652 F01b/S330.7: through Rev32.8 this paragraph derived the ray from “a group average over a symmetry that acts transitively on the channels”, which is unavailable for both projectors.)"
 },
 "caution": "This UV coefficient ray does not predict equal low-energy masses or select a symmetry-breaking compensator. Retention is not protection: excluding an unequal quartet is a separate claim, and it holds only under the trivial multiplicity-one premise, which Appendix K p.234 states as a premise exhibited on the model group S4 and does not derive for the registered four-channel action.",
 "candidate_ids": [
  "C2-046"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "type": "related_to",
   "target": "LIB2-111"
  }
 ],
 "url": "/library-v2/LIB2-113/",
 "content_sha256": "36236cbc0673f708d32f73e1b72963cd3acbd1dcb1c25c686772f144c071335e",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}