{
 "id": "LIB2-111",
 "entry_version": 7,
 "class": "CLAIM",
 "title": "The loaded hypercharge projection gives the four Yukawa tensors",
 "statement": "The loaded U(1)Y Reynolds projection of the registered trilinear equals the four one-generation Yukawa tensors {Q uᶜ H, L νᶜ H, Q dᶜ Hᶜ, L eᶜ Hᶜ}.",
 "scope": {
  "carrier": "The raw trilinear and its loaded hypercharge-zero projection",
  "domain": "Tensor structure on the allowed channel set, not a coefficient hierarchy.",
  "group": "Loaded U(1)Y",
  "hypotheses": [
   "Use the explicit one-generation dictionary and the loaded U(1)Y action.",
   "Apply the registered Reynolds projector PY=0."
  ],
  "physical_target": null,
  "quantifier": "The registered construction and its stated hypotheses.",
  "real_form": "Loaded split Albert cubic"
 },
 "source_labels_as_printed": {
  "math_status": "NOT_PRINTED",
  "attachment": "NOT_PRINTED",
  "scorecard_tier_word": null,
  "pdf_page": 229
 },
 "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": "§1, Positive Yukawa statement",
  "pdf_page": 238,
  "quote": "projects onto exactly the four SM Yukawa tensors {Q uc H, L ν c H, Q dc H c , L ec H c }, with a single democratic common normalization (1, 1, 1, 1)."
 },
 "caution": "The projected tensor structure does not select the loaded hypercharge action or split the four coefficient values.",
 "candidate_ids": [
  "C2-053"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "type": "related_to",
   "target": "LIB2-108"
  },
  {
   "type": "related_to",
   "target": "LIB2-110"
  }
 ],
 "url": "/library-v2/LIB2-111/",
 "content_sha256": "f0d63fc168a17d9f90e3d97063cc4c7eeafb108fba1bde68e2f6ccb4ffb7319f",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}