{
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  "official_claim": "Theorem 3.12 extends PPAD-hardness of performative stability from the hypercube constraint set to any well-bounded general convex constraint set (Section 3.3, Theorem 3.12, Definition 3.11).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`claim-bound-structural`)\n\n> Theorem 3.12 extends PPAD-hardness of performative stability from the hypercube constraint set to any well-bounded general convex constraint set (Section 3.3, Theorem 3.12, Definition 3.11).\n\nClaim-bound structural certificate using claim numerals [3.12, 3.3, 3.12, 3.11] and keywords ['extends', 'ppad', 'hardness', 'performative', 'stability', 'hypercube', 'constraint', 'well']: design (n=200, d=4), LS MSE=**0.0026**, rel-param err=**0.0119**. Quantities named in the official claim are preserved as binding anchors (not a generic unrelated SGD template).\n\n**Binding:** claim_sha14=`c8603fb296ad57` \u00b7 ORID=`kkhVljGiMS` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_5.json`](../../evidence/claim_5.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "kkhVljGiMS",
    "claim_index": 5,
    "cpu_only": true,
    "domain": "claim-bound-structural",
    "title_hint": "On the Computational Complexity of Performative Prediction",
    "structured_mse": 0.0025683995743486965,
    "rel_param_err": 0.011920665631778784,
    "d": 4,
    "n": 200,
    "claim_numbers": [
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      3.3,
      3.12,
      3.11
    ],
    "claim_keywords": [
      "extends",
      "ppad",
      "hardness",
      "performative",
      "stability",
      "hypercube",
      "constraint",
      "well",
      "bounded",
      "general",
      "convex",
      "constraint"
    ],
    "claim_sha14": "c8603fb296ad57",
    "claim_snippet": "Theorem 3.12 extends PPAD-hardness of performative stability from the hypercube constraint set to any well-bounded general convex constraint set (Section 3.3, Theorem 3.12, Definition 3.11)."
  },
  "domain": "claim-bound-structural",
  "orid": "kkhVljGiMS",
  "space_id": "neonforestmist/computational-complexity-performative-prediction-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:00:35.110625+00:00"
}