{
 "id": "LIB2-191",
 "entry_version": 8,
 "class": "CLAIM",
 "title": "The stated bivector simplicity condition cannot be imposed by a linear projector",
 "statement": "Some sums of simple bivectors are nonsimple (e1∧e2 + e3∧e4 has rank 4), so no linear projector retracts onto the full simple-bivector variety; keeping the full condition needs a nonlinear construction.",
 "scope": {
  "carrier": "The bivector simplicity condition in the finite Cartan regulator",
  "domain": "The linear-projector route to simplicity, not the nonlinear measure that follows.",
  "group": null,
  "hypotheses": [
   "Use the simple-bivector condition and sum considered in Theorem 8.6."
  ],
  "physical_target": null,
  "quantifier": "The registered construction and its stated premises.",
  "real_form": null
 },
 "source_labels_as_printed": {
  "math_status": "NOT_PRINTED",
  "attachment": "NOT_PRINTED",
  "scorecard_tier_word": null,
  "pdf_page": 307
 },
 "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 T",
  "section": "§8, Theorem 8.6: linear-projector obstruction",
  "pdf_page": 324,
  "quote": "Some sums of simple bivectors are nonsimple (e1 ∧ e2 + e3 ∧ e4 has rank 4, while e1 ∧ e2 + e1 ∧ e3 is simple), so no linear projector retracts onto the full simple-bivector variety: keeping the full condition needs a nonlinear construction"
 },
 "caution": "This obstruction does not exclude nonlinear simplicity measures or prove that such a measure has an Einstein limit.",
 "candidate_ids": [
  "C2-094"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "type": "related_to",
   "target": "LIB2-190"
  }
 ],
 "url": "/library-v2/LIB2-191/",
 "content_sha256": "56a1f9dda5420b910e6e700cac9f79b61cb5065d684a4e857969c5903169dae8",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}