{
 "id": "LIB2-077",
 "entry_version": 10,
 "class": "CLAIM",
 "title": "The unitary matter-colour class has no image-compatible adjoint",
 "statement": "For the registered unitary matter-colour class, the invariant embedding-tensor space has dimension 140, and the union of its rowspaces has rank 125, its eight missing directions being exactly the su(3) adjoint.",
 "scope": {
  "carrier": "Inv_su(3),unitary(912) and its combined rowspace in the 133",
  "domain": "Rowspace orthogonality to the required colour adjoint.",
  "group": "su(3)",
  "hypotheses": [
   "The unitary class is 8 = 3 ⊕ 5·1.",
   "Use the registered invariant embedding-tensor space and rowspace conventions."
  ],
  "physical_target": null,
  "quantifier": "The specified invariant space for this embedding class.",
  "real_form": "Compact unitary-class su(3) in su(8)"
 },
 "source_labels_as_printed": {
  "math_status": "NOT_PRINTED",
  "attachment": "NOT_PRINTED",
  "scorecard_tier_word": null,
  "pdf_page": 176
 },
 "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": "§3, Leg A: invariant-space dimension and rowspace rank",
  "pdf_page": 182,
  "quote": "dimension 140, matching the character prediction 140 = 2·15 (36⊕36)+2·55 (420⊕420) exactly (singular-value gap 8.9 × 1013 ). The union of the rowspaces of all invariant Θ has rank 125,"
 },
 "caution": "This embedding-class result does not identify a physical colour action elsewhere or supply a derivation of the compact Standard-Model boundary.",
 "candidate_ids": [
  "C2-038"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "type": "related_to",
   "target": "LIB2-076"
  }
 ],
 "url": "/library-v2/LIB2-077/",
 "content_sha256": "b99eb22b4883307896b8e25a1799f9c3b86038bb8c1456719589fcb0c982ed95",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}