{
 "id": "LIB2-192",
 "entry_version": 10,
 "class": "CLAIM",
 "title": "A soft positive simplicity weight exists at finite regulator",
 "statement": "At finite regulator, a positive nonlinear simplicity weight exists on the compact fixed-norm bivector domain (a sum-of-squares penalty in the five Pfaffian minors), with reflection positivity by the standard paired-multiplication argument at argument tier.",
 "scope": {
  "carrier": "The compact fixed-norm bivector domain and its soft nonlinear simplicity weight at finite regulator",
  "domain": "Finite-regulator weight existence, not a hard Pfaffian-variety measure and not a continuum gravitational universality result.",
  "group": null,
  "hypotheses": [
   "Use the fixed-norm bivector domain, the sum-of-squares penalty in the five Pfaffian minors and the paired-multiplication reflection-positivity argument (argument tier) of Appendix T."
  ],
  "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": "IN_REVIEW",
 "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)",
 "evidence_status": [
  {
   "kind": "registry",
   "availability": "shipped"
  }
 ],
 "primary_source": {
  "component": "Appendix T",
  "section": "§8, Theorem 8.6: nonlinear simplicity measure",
  "pdf_page": 324,
  "quote": "A positive nonlinear simplicity weight exists at finite regulator: the sum-of-squares penalty exp(−λ i pi (B)2 ) in the five Pfaffian minors pi , on the fixed-norm P bivector domain (compact, so 0 < Z < ∞ for every λ ≥ 0), with reflection positivity by the standard paired-multiplication argument (argument-tier; s922 T6 notes)."
 },
 "caution": "The weight is soft: its support is the whole fixed-norm domain, and the Pfaffian variety is reached only in the hard-constraint limit, which is not taken. Finite-regulator existence does not establish Einstein universality or the continuum renormalization-group limit.",
 "candidate_ids": [
  "C2-094"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "type": "related_to",
   "target": "LIB2-170"
  },
  {
   "type": "related_to",
   "target": "LIB2-189"
  },
  {
   "type": "related_to",
   "target": "LIB2-191"
  },
  {
   "type": "rests_on_premise",
   "target": "PRM-014"
  }
 ],
 "url": "/library-v2/LIB2-192/",
 "content_sha256": "a3505dc317432d3c3bede5485a56ca391da7c6119a3ade7b8ecf516601fc883e",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}