{
 "id": "LIB2-082",
 "entry_version": 8,
 "class": "CLAIM",
 "title": "The extra compact Cartan is the B−L charge direction",
 "statement": "For the registered completion filters, the Yukawa-neutrality and anomaly equations have, modulo the hypercharge direction, a one-dimensional extra-Cartan solution space, whose Higgs-doublet-neutral representative is (1,−1,−1,−3,3,3) = 3(B−L).",
 "scope": {
  "carrier": "Extra compact Cartan charges on the fixed matter package",
  "domain": "The unique surviving extra charge direction under the completion filters.",
  "group": "U(1)B−L",
  "hypotheses": [
   "Use the fixed field dictionary, Yukawa-neutrality equations and anomaly system of Theorem 4.1."
  ],
  "physical_target": null,
  "quantifier": "The stated extra-Cartan solution space.",
  "real_form": "Compact low-energy completion"
 },
 "source_labels_as_printed": {
  "math_status": "NOT_PRINTED",
  "attachment": "NOT_PRINTED",
  "scorecard_tier_word": null,
  "pdf_page": 177
 },
 "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 F",
  "section": "§4, Theorem 4.1(2): extra Cartan",
  "pdf_page": 183,
  "quote": "the extra compact Cartan is unique: modulo the existing hypercharge direction the extra solution space of the Yukawa- neutrality + anomaly system is one-dimensional, and in the Higgs-doublet-neutral representative it is spanned by (1, −1, −1, −3, 3, 3) = 3(B−L)"
 },
 "caution": "The unique extra charge direction does not establish that its gauge boson exists or remove the empirical premise used to exclude it.",
 "candidate_ids": [
  "C2-043"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "type": "related_to",
   "target": "LIB2-081"
  }
 ],
 "url": "/library-v2/LIB2-082/",
 "content_sha256": "be2416cf706a627c2f05ee5a39e5613b922994a92a1c9d03b4f6645203a3b9df",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}