{
 "id": "LIB2-156",
 "entry_version": 8,
 "class": "CLAIM",
 "title": "The direct Markov-second-moment repair has the wrong sign",
 "statement": "The canonical connected Markov second moment is non-negative, while the required binding correction at n = 6,7 is negative; the declared direct second-moment repair lacks the negative energy coefficient needed to reverse the sign.",
 "scope": {
  "carrier": "The connected normalized Markov second moment in Aφ = ATLφ/⟨f4⟩",
  "domain": "The direct second-moment binding-repair class, not all possible energy attachments.",
  "group": null,
  "hypotheses": [
   "Use the canonical connected normalized Markov second moment of the registered mirror-odd circulation.",
   "The required correction is the source's negative six-to-seven-cell deficit."
  ],
  "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": 131
 },
 "house_tier": null,
 "review_state": "PUBLISHED",
 "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)",
 "evidence_status": [
  {
   "kind": "computational",
   "availability": "unknown"
  }
 ],
 "primary_source": {
  "component": "Paper 9",
  "section": "§9, Direct annular second-moment attachment",
  "pdf_page": 136,
  "quote": "the canonical connected Markov second moment is non-negative, whereas the required n = 6, 7 binding correction is negative, so the annular order does not derive the negative energy coefficient that would reverse the sign;"
 },
 "caution": "This excludes the declared direct attachment, not every annular operator or an independently derived negative energy map.",
 "candidate_ids": [
  "C2-083",
  "C2-128"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "type": "related_to",
   "target": "LIB2-154"
  },
  {
   "type": "related_to",
   "target": "LIB2-144"
  }
 ],
 "url": "/library-v2/LIB2-156/",
 "content_sha256": "4e0b4dc922aefbdd89a4fb49603b6465f655450c474a28bbd613f20405e623d8",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}