{
 "id": "LIB2-044",
 "entry_version": 7,
 "class": "CLAIM",
 "title": "A beat-invariant potential in the declared KN class cannot isolate the dark ray",
 "statement": "In the declared unshifted zero-level quadratic-carrier Kempf–Ness class, no beat-invariant potential isolates the selector ray [W0].",
 "scope": {
  "carrier": "The beat orbit and selector ray [W0]",
  "domain": "The source-stated beat-transitivity obstruction; separate from the Hessian-rank bound.",
  "group": null,
  "hypotheses": [
   "Use the declared unshifted zero-level quadratic-carrier Kempf–Ness class.",
   "The potential is beat-invariant."
  ],
  "physical_target": null,
  "quantifier": "The declared class only.",
  "real_form": null
 },
 "source_labels_as_printed": {
  "math_status": "NOT_PRINTED",
  "attachment": "NOT_PRINTED",
  "scorecard_tier_word": null,
  "pdf_page": 167
 },
 "house_tier": null,
 "review_state": "PUBLISHED",
 "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)",
 "evidence_status": [
  {
   "kind": "registry",
   "availability": "shipped"
  }
 ],
 "primary_source": {
  "component": "Appendix E",
  "section": "§6(vii), Beat-transitivity obstruction",
  "pdf_page": 174,
  "quote": "no beat-invariant KN potential isolates [W0 ] (the beat-transitivity no-go)."
 },
 "caution": "A beat-breaking spurion, dropping the clock circle or leaving the KN family exits this declared class; none is ruled out universally.",
 "candidate_ids": [
  "C2-108"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "type": "related_to",
   "target": "LIB2-043"
  },
  {
   "type": "related_to",
   "target": "LIB2-023"
  },
  {
   "type": "cited_by_section",
   "target": "E-C04.2.claims-used"
  },
  {
   "type": "cited_by_section",
   "target": "E-C04.2.derivation"
  },
  {
   "type": "cited_by_section",
   "target": "E-C04.2.sources-receipt"
  }
 ],
 "url": "/library-v2/LIB2-044/",
 "content_sha256": "d4e98a452d2f50b944fa8f88e65e1b73115b22acf971b839d2239607beda1d5c",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}