{
  "public_id": "TA-2026-001",
  "version": "1.0",
  "released": "2026-11-06",
  "status": "published",
  "sample": false,
  "kind": "negative",
  "track": "matching_social_choice",
  "title": "Kamada and Kojima (2018)",
  "headline": "No defect was found in Theorems 1 or 2 within the stated audit scope. This is not a proof that the theorems are correct.",
  "work": {
    "authors": [
      "Yuichiro Kamada",
      "Fuhito Kojima"
    ],
    "title": "Stability and strategy-proofness for matching with constraints: A necessary and sufficient condition",
    "venue": "Theoretical Economics",
    "year": 2018,
    "volume": "13",
    "pages": "761–793",
    "doi": "10.3982/TE2717"
  },
  "claims": [
    {
      "id": "c1",
      "label": "Theorem 1",
      "kind": "theorem",
      "role": "main",
      "page": "771",
      "gist": "A hierarchical region family admits a stable, doctor-strategy-proof mechanism.",
      "statement": "If the region family is a hierarchy, there exists a mechanism that is stable and strategy-proof for doctors.",
      "conditions": [
        "finite doctors and hospitals with strict doctor rankings",
        "responsive hospital preferences and regional quotas",
        "admissible substitutable regional quasi-choice preferences",
        "a fixed region family containing singleton and grand regions"
      ],
      "quantifiers": "The mechanism must work across the paper's admitted regional caps, regional preferences and agent preference profiles for the fixed doctor, hospital and region sets.",
      "result": {
        "outcome": "no_defect_found",
        "depth": "deep_audit",
        "summary": "No counterexample or nontrivial proof gap survived the recorded audit of the hierarchy direction.",
        "search_scope": "The audit reconstructed the hierarchy mechanism and checked archived finite suites covering 4,284 hierarchical markets, 1,638,144 outcomes and 59,927,040 unilateral-deviation checks, with zero recorded failures. The proof logic and theorem quantifiers were also reviewed against the published version.",
        "limits": "The finite search is selective and does not prove unrestricted sufficiency. The publication review reconciled the archived counts and source logic but did not rerun all 59,927,040 deviation checks."
      },
      "vor_check": {
        "level": "full",
        "pages": "769–772",
        "detail": "The stability definition, mechanism quantifiers and Theorem 1 were checked on rendered pages of the published version."
      },
      "checks": [],
      "reproduction": {
        "result": "partial",
        "detail": "The archived package integrity and reported counts were reconciled; the full historical computation was not rerun during publication review."
      },
      "novelty": null
    },
    {
      "id": "c2",
      "label": "Theorem 2",
      "kind": "theorem",
      "role": "main",
      "page": "772",
      "gist": "For a non-hierarchical region family, no stable, doctor-strategy-proof mechanism works across the full admitted domain.",
      "statement": "If the region family is not a hierarchy, no mechanism is stable and strategy-proof for doctors across the paper's admitted domain.",
      "conditions": [
        "finite doctors and hospitals with strict doctor rankings",
        "responsive hospital preferences and regional quotas",
        "admissible substitutable regional quasi-choice preferences",
        "a fixed region family containing singleton and grand regions"
      ],
      "quantifiers": "The impossibility concerns one mechanism required to work across the full admitted domain for the fixed doctor, hospital and region sets; it is not a claim that every fixed non-hierarchical profile is itself impossible.",
      "result": {
        "outcome": "no_defect_found",
        "depth": "deep_audit",
        "summary": "No counterexample or nontrivial proof gap survived the recorded audit of the non-hierarchy impossibility direction.",
        "search_scope": "The audit checked the paper's decisive three-profile non-hierarchy example: at the baseline there are two stable matchings, and whichever one a putative stable mechanism selects, one doctor can misreport so that the other becomes uniquely stable and is strictly better under that doctor's true ranking. An exact certificate, a separate finite stability checker and a full 576-report stable-selection model corroborate the case split.",
        "limits": "The theorem is about a mechanism over the full admitted domain, not impossibility for every fixed non-hierarchical profile. The finite certificate supports the decisive construction but does not by itself prove every step of the general theorem."
      },
      "vor_check": {
        "level": "full",
        "pages": "772–774, 787–788",
        "detail": "Theorem 2, the three-profile example and the general non-hierarchy proof were checked on rendered pages of the published version."
      },
      "checks": [],
      "reproduction": {
        "result": "partial",
        "detail": "The archived exact certificate and model outputs were reconciled and the logical case split was rechecked; the entire historical computation was not rerun during publication review."
      },
      "novelty": null
    }
  ],
  "author_position": {
    "position": "not_contacted",
    "summary": null
  },
  "correction": null,
  "evidence": {
    "package_doi": null,
    "package_sha256": null,
    "licence": "No public evidence package released.",
    "files": []
  },
  "history": [
    {
      "date": "2026-10",
      "type": "audit",
      "label": "Deep audit completed: no defect found within the recorded scope"
    },
    {
      "date": "2026-10-31",
      "type": "source",
      "label": "Full published-version source check completed"
    },
    {
      "date": "2026-11-06",
      "type": "release",
      "label": "Record version 1.0 approved for release"
    }
  ],
  "challenges": [],
  "changelog": [
    {
      "version": "1.0",
      "date": "2026-11-06",
      "change": "First release."
    }
  ],
  "statements": {
    "ai_use": "AI systems were used in the historical audit and in later review. The record distinguishes AI and computational evidence from human verification and does not treat AI agreement as human confirmation."
  }
}