{
 "id": "LIB2-010",
 "entry_version": 10,
 "class": "CLAIM",
 "title": "The algebra generated by the complementary tangent plane",
 "statement": "The missing-16 plane generates a 28-dimensional algebra identified with so(4,4), whose compact part is so(4) ⊕ so(4) of dimension 12.",
 "scope": {
  "carrier": "g′ = [16,16] ⊕ 16 generated by the registered complementary plane",
  "domain": "Generated Lie-algebra identification; its associated symmetric-space identification is local.",
  "group": "SO(4,4)",
  "hypotheses": [
   "The registered plane, brackets and source normalization are used."
  ],
  "physical_target": null,
  "quantifier": "The algebra generated by this plane.",
  "real_form": "so(4,4) with compact part so(4) ⊕ so(4)"
 },
 "source_labels_as_printed": {
  "math_status": "NOT_PRINTED",
  "attachment": "NOT_PRINTED",
  "scorecard_tier_word": null,
  "pdf_page": 181
 },
 "house_tier": null,
 "review_state": "IN_REVIEW",
 "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)",
 "evidence_status": [
  {
   "kind": "registry",
   "availability": "shipped"
  }
 ],
 "primary_source": {
  "component": "Appendix F",
  "section": "§5.3, Generated-algebra identification",
  "pdf_page": 187,
  "quote": "Cartan character +4 — a tuple that by itself does not distinguish so(4, 4) from g2(2) ⊕ g2(2)"
 },
 "caution": "This local Lie-algebra identification does not prove geodesic completeness, embedding closedness or a global quotient identification.",
 "candidate_ids": [
  "C2-033"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "type": "related_to",
   "target": "LIB2-009"
  },
  {
   "type": "cited_by_section",
   "target": "E-C03.2.claims-used"
  },
  {
   "type": "cited_by_section",
   "target": "E-C03.2.computations"
  },
  {
   "type": "cited_by_section",
   "target": "E-C03.2.derivation"
  },
  {
   "type": "cited_by_section",
   "target": "E-C03.2.prior-art"
  },
  {
   "type": "cited_by_section",
   "target": "E-C03.2.sources-receipt"
  }
 ],
 "url": "/library-v2/LIB2-010/",
 "content_sha256": "88ab4c09fac97ff248ef3522e75e772160c7c4dd5b39112ff6b64088e7f00dd7",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}