{
 "id": "LIB2-185",
 "entry_version": 8,
 "class": "CLAIM",
 "title": "The rank-two support certificate excludes a rank-five extension at the MOS tier",
 "statement": "An ambient rank-5 extension exists, but the record-support condition excludes it at the printed MOS tier by an exact rank-two support certificate.",
 "scope": {
  "carrier": "The record-support constraint and an ambient linear-algebra extension",
  "domain": "The tier-local support obstruction, not nonexistence of the ambient extension.",
  "group": null,
  "hypotheses": [
   "Retain the record-support condition of the printed MOS quotient tier."
  ],
  "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": 316
 },
 "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": "§15.3, Ambient extension and tier-local obstruction",
  "pdf_page": 334,
  "quote": "A rank-5 extension exists as ambient linear algebra, but the record-support condition forbids it at the printed MOS tier by an exact rank-two support certificate [A1560]."
 },
 "caution": "The support certificate does not exclude a microscopic map outside the printed quotient tier or deny the ambient rank-five construction.",
 "candidate_ids": [
  "C2-135"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "type": "related_to",
   "target": "LIB2-175"
  },
  {
   "type": "related_to",
   "target": "LIB2-184"
  }
 ],
 "url": "/library-v2/LIB2-185/",
 "content_sha256": "a753bba79e682b499380b8ab998465a50b357e5d1efcc911197d6d7723d0379c",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}