{
 "id": "LIB2-148",
 "entry_version": 7,
 "class": "CLAIM",
 "title": "The composition ladder is a finite trace invariant",
 "statement": "The finite composition weights obey Tn = (n − 2) + εn with εn = trϕ(Rn), where the trace is taken on the residual boundary-circulation class in the stated Temperley–Lieb quotient.",
 "scope": {
  "carrier": "The n-gon flip graph and residual boundary-circulation class",
  "domain": "The finite trace weight, before its declared binding-energy attachment.",
  "group": null,
  "hypotheses": [
   "Use the quotient TLφ/⟨f4⟩ and its registered Markov trace."
  ],
  "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": 129
 },
 "house_tier": null,
 "review_state": "PUBLISHED",
 "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)",
 "evidence_status": [
  {
   "kind": "registry",
   "availability": "shipped"
  }
 ],
 "primary_source": {
  "component": "Paper 9",
  "section": "§6, Equation (3): trace ladder",
  "pdf_page": 133,
  "quote": "Tn = (n − 2) + εn , εn = trϕ (Rn )"
 },
 "caution": "The finite trace law does not on its own derive a binding energy or a continuum Yang–Mills functor.",
 "candidate_ids": [
  "C2-077"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "type": "related_to",
   "target": "LIB2-143"
  },
  {
   "type": "related_to",
   "target": "LIB2-144"
  }
 ],
 "url": "/library-v2/LIB2-148/",
 "content_sha256": "193fbb8203b218b098f4475e0d192dc59f277ae3aef800a16d625ce616f0bc63",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}