{
 "id": "LIB2-076",
 "entry_version": 7,
 "class": "CLAIM",
 "title": "The enumerated compact embeddings fail the simultaneous-adjoint test",
 "statement": "For every one of the 21 enumerated faithful compact su(3) ⊕ su(2) classes, the restricted 56 lacks either the colour adjoint (8,1) or the weak adjoint (1,3).",
 "scope": {
  "carrier": "56 restricted through the enumerated faithful branchings of the su(8) fundamental",
  "domain": "The simultaneous-adjoint multiplicity test, not an independently certified domain-wide completeness result.",
  "group": "su(3) ⊕ su(2)",
  "hypotheses": [
   "Use the 21 faithful classes enumerated in Appendix F §2.",
   "The carrier restricts as Λ²8 ⊕ Λ²8̄."
  ],
  "physical_target": null,
  "quantifier": "Every class in the printed finite census.",
  "real_form": "Compact su(3) ⊕ su(2) inside su(8)"
 },
 "source_labels_as_printed": {
  "math_status": "NOT_PRINTED",
  "attachment": "NOT_PRINTED",
  "scorecard_tier_word": null,
  "pdf_page": 175
 },
 "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 F",
  "section": "§2, Proof step L4: adjoint multiplicities",
  "pdf_page": 181,
  "quote": "for every one of the 21 faithful classes, mult(8, 1) = 0 or mult(1, 3) = 0 in 56 ↓ ι = Λ2 8 ⊕ Λ2 8̄."
 },
 "caution": "This record states the finite census; it neither independently verifies the broader all-frame theorem nor excludes noncompact real forms.",
 "candidate_ids": [
  "C2-037"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [],
 "url": "/library-v2/LIB2-076/",
 "content_sha256": "a16cb954b5582ef38db9579c37914f1d04ba8316b11f6d31ff6d42efd7a7ba58",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}