{
 "id": "LIB2-107",
 "entry_version": 8,
 "class": "CLAIM",
 "title": "The signed metric-weighted residue cannot supply the positive seven count",
 "statement": "For a subcollection of registered g-orthonormal Im Os channels, the signed residue equals the positive-minus-negative channel count and lies in [−4,+3], excluding 7 as that metric-weighted residue.",
 "scope": {
  "carrier": "Subcollections of g-orthonormal imaginary split-octonion channels",
  "domain": "The specific metric-weighted residue route; unweighted index and other physical realizations are different objects.",
  "group": null,
  "hypotheses": [
   "The imaginary split-octonion metric has signature (3,4).",
   "Use the signed channel-count residue of Lemma 8.3, not arbitrary independent channel weights."
  ],
  "physical_target": null,
  "quantifier": "Any subcollection of the registered g-orthonormal channels.",
  "real_form": "Split octonions Os"
 },
 "source_labels_as_printed": {
  "math_status": "NOT_PRINTED",
  "attachment": "NOT_PRINTED",
  "scorecard_tier_word": null,
  "pdf_page": 212
 },
 "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 I",
  "section": "§8, Lemma 8.3: signed-residue range",
  "pdf_page": 222,
  "quote": "The signed residue over any sub- collection of g-orthonormal channels equals (#positive − #negative) and therefore lies in the closed range [−4, +3]"
 },
 "caution": "This bound does not refute the finite trace/index theorem or exclude every non-residue physical realization of the ratio.",
 "candidate_ids": [
  "C2-044",
  "C2-054"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "type": "related_to",
   "target": "LIB2-053"
  },
  {
   "type": "cited_by_section",
   "target": "E-C08.2.claims-used"
  },
  {
   "type": "cited_by_section",
   "target": "E-C08.2.definitions-conventions"
  },
  {
   "type": "cited_by_section",
   "target": "E-C08.2.prior-art"
  }
 ],
 "url": "/library-v2/LIB2-107/",
 "content_sha256": "8a6f2f9f43e7aec6849f386ba6274e0802fb0411c6903473689330c122319b14",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}