{
  "public_id": "TA-2026-002",
  "version": "1.0",
  "released": "2026-11-07",
  "status": "published",
  "sample": false,
  "kind": "defect",
  "track": "mechanism_design",
  "title": "Gavan and Penta (2025)",
  "headline": "The mechanism displayed in the proof of Theorem 3 admits an unwanted Nash equilibrium in an admitted instance. The existential conclusion of Theorem 3 is not refuted.",
  "work": {
    "authors": [
      "Malachy J. Gavan",
      "Antonio Penta"
    ],
    "title": "Safe implementation",
    "venue": "Theoretical Economics",
    "year": 2025,
    "volume": "20(4)",
    "pages": "1285–1322",
    "doi": "10.3982/TE5983"
  },
  "claims": [
    {
      "id": "c1",
      "label": "Theorem 3 proof construction",
      "kind": "construction",
      "role": "main",
      "page": "1299; 1310–1311",
      "gist": "The four-rule message mechanism displayed in the proof implements the correspondence throughout the stated domain.",
      "statement": "The four-rule message mechanism displayed in the proof of Theorem 3 implements F under the theorem's hypotheses for every admissible integer 1 ≤ k < n/2.",
      "conditions": [
        "at least three agents",
        "1 ≤ k < n/2",
        "strong comonotonicity",
        "safe no-veto",
        "the published priority-ordered Rules (i)–(iv)"
      ],
      "quantifiers": "Every admitted environment satisfying the hypotheses of Theorem 3 and every admissible safety level k.",
      "result": {
        "outcome": "defect_found",
        "candidate_status": "confirmed",
        "defect_class": "construction_or_algorithm_fails",
        "affects": "lemma_or_proof_step",
        "depth": "deep_audit",
        "summary": "The displayed mechanism can select an outcome outside F at a pure Nash equilibrium.",
        "witness": "With one state, outcomes {a,b}, F={b}, three agents and k=1, let agents 1 and 2 prefer b to a and agent 3 prefer a to b. At messages ((a,s,1),(a,s,1),(b,s,1)), the printed rules select a, outside F. The two agents who prefer b cannot profitably change the outcome by switching their report, and agent 3 already receives her preferred outcome.",
        "tested": "The minimal three-agent witness was checked against the published Rules (i)–(iv), the theorem's stated assumptions and the legal unilateral reports. Historical finite checks and a separate informed AI validation corroborate the construction failure.",
        "not_claimed": [
          "The existential conclusion of Theorem 3 is not claimed to be false.",
          "The record does not claim that no alternative mechanism can safely implement F.",
          "The record does not publish or assess any private proposed correction."
        ],
        "repair": "none_proposed"
      },
      "vor_check": {
        "level": "full",
        "pages": "1298–1299, 1310–1311",
        "detail": "The definitions, Theorem 3, the displayed Rules (i)–(iv) and the decisive proof step were checked on rendered pages of the publisher-hosted version of record."
      },
      "checks": [
        {
          "kind": "ai_recheck",
          "date": "2026-10",
          "result": "confirms",
          "detail": "A separate informed AI validation checked the analytic failure family against the printed mechanism.",
          "session": "informed"
        },
        {
          "kind": "private_human_confirmation",
          "date": "2026-10",
          "result": "confirms",
          "detail": "A qualifying human confirmation is recorded in the private research file. Its source and correspondence are not disclosed."
        }
      ],
      "novelty": null
    }
  ],
  "author_position": {
    "position": "not_disclosed",
    "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": "Construction defect identified and separately rechecked"
    },
    {
      "date": "2026-10-31",
      "type": "source",
      "label": "Full published-version source check completed"
    },
    {
      "date": "2026-11-07",
      "type": "release",
      "label": "Record version 1.0 released"
    }
  ],
  "challenges": [],
  "changelog": [
    {
      "version": "1.0",
      "date": "2026-11-07",
      "change": "First release."
    }
  ],
  "statements": {
    "ai_use": "AI systems were used for discovery and separate hostile rechecking. Confirmation also includes a qualifying human check recorded privately. Private correspondence is not disclosed, and AI agreement is not treated as human verification."
  }
}