{
 "id": "LIB2-039",
 "entry_version": 7,
 "class": "CLAIM",
 "title": "A fixed-grade cubic/current law cannot detect both dark directions",
 "statement": "In the declared fixed-grade cubic/current class, restriction to grade +2 gives rank 1 for Z ↦ P27 Z P27, so it cannot provide rank-two detection of the registered dark fibre.",
 "scope": {
  "carrier": "The dark fibre restricted to the fixed +2 grade",
  "domain": "Rank-two detection inside a fixed grade; the embedding-tensor class was not decided.",
  "group": null,
  "hypotheses": [
   "The detector stays inside the fixed grade and uses the declared cubic/current class.",
   "Both registered dark directions are required for rank-two detection."
  ],
  "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": "computational",
   "availability": "unknown"
  }
 ],
 "primary_source": {
  "component": "Appendix E",
  "section": "§6(iv), Fixed-grade detection obstruction",
  "pdf_page": 173,
  "quote": "The fixed-grade cubic/current class is closed negative for rank-two detection (s1005–s1006)."
 },
 "caution": "This fixed-grade exclusion is not an embedding-tensor no-go; that separate class was scoped out for lack of a convention-certified branching artifact.",
 "candidate_ids": [
  "C2-105"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "type": "related_to",
   "target": "LIB2-036"
  },
  {
   "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/LIB2-039/",
 "content_sha256": "2a70a1aa8b3bc411025169b35c38b30059e7baaacd0d85ab6a12e8b845fba4fa",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}