{
 "id": "LIB2-043",
 "entry_version": 7,
 "class": "CLAIM",
 "title": "Unshifted quadratic Kempf–Ness potentials fail the selector-rank test",
 "statement": "In the declared unshifted zero-level quadratic-carrier Kempf–Ness class, rank Hess0∥µK∥² ≤ dim K ≤ 63 < 69 = rank QT, so this class cannot reproduce the selector Hessian.",
 "scope": {
  "carrier": "The unshifted zero-level quadratic carrier and its moment-map-square potential",
  "domain": "The unshifted zero-level quadratic-carrier class only.",
  "group": "K in the declared class",
  "hypotheses": [
   "Use the predeclared Kempf–Ness class cited in Appendix E §6(vii).",
   "The target is the registered selector Hessian QT."
  ],
  "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), Unshifted Kempf–Ness rank bound",
  "pdf_page": 174,
  "quote": "rank Hess0 ∥µK ∥2 ≤ dim K ≤ 63 < 69 = rank QT (the rank no-go)"
 },
 "caution": "Central shifts on proper subgroups or departure from the declared carrier/potential class are not excluded by this bound.",
 "candidate_ids": [
  "C2-108"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "type": "related_to",
   "target": "LIB2-027"
  },
  {
   "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.prior-art"
  },
  {
   "type": "cited_by_section",
   "target": "E-C04.2.sources-receipt"
  }
 ],
 "url": "/library-v2/LIB2-043/",
 "content_sha256": "aaf434e33d4198b90c2d62901d11f78c9252c172d75b205a614feee63ab8cd3a",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}