{
 "id": "LIB2-175",
 "entry_version": 12,
 "class": "CLAIM",
 "title": "The supported MOS quotient has rank three and relative rank two",
 "statement": "The supported observation quotient ΠMOS has rank 3 and relative rank 2 < 5; it is not the full microscopic loading.",
 "scope": {
  "carrier": "The supported MOS observation quotient from paired and annular carriers",
  "domain": "The finite supported quotient, not the microscopic support-restoring map.",
  "group": null,
  "hypotheses": [
   "Use the registered pair coisometry, Hodge frame and annular Fourier support."
  ],
  "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": 310
 },
 "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": "§11, Theorem 11.2: partial isometry",
  "pdf_page": 328,
  "quote": "exact partial isometry (Π̃Π̃T = Pann , Π̃T Π̃ = PV4 ) killing all pair-difference modes;"
 },
 "caution": "The finite quotient does not restore missing microscopic modes or discharge the full observation-map construction.",
 "candidate_ids": [
  "C2-092"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "type": "related_to",
   "target": "LIB2-174"
  }
 ],
 "url": "/library-v2/LIB2-175/",
 "content_sha256": "add96a1abbf9ad86a08030c878f8f28cd98e63ae1f3d007652bfead8b9048c46",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}