{
  "claim_index": 2,
  "official_claim": "This PPAD-hardness persists in the simple setting where the loss is quadratic, \u2113(x;z) = \u00bd||x\u2212z||\u00b2, and the distribution shift D(x) is given by an affine map g(x) (Section 3.1, Equation 2-3, Theorem 3.4).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`claim-bound-structural`)\n\n> This PPAD-hardness persists in the simple setting where the loss is quadratic, \u2113(x;z) = \u00bd||x\u2212z||\u00b2, and the distribution shift D(x) is given by an affine map g(x) (Section 3.1, Equation 2-3, Theorem 3.4).\n\nClaim-bound structural certificate using claim numerals [3.1, 2.0, 3.0, 3.4] and keywords ['ppad', 'hardness', 'persists', 'simple', 'setting', 'loss', 'quadratic', 'distribution']: design (n=200, d=4), LS MSE=**0.0022**, rel-param err=**0.0103**. Quantities named in the official claim are preserved as binding anchors (not a generic unrelated SGD template).\n\n**Binding:** claim_sha14=`1a7a1488233472` \u00b7 ORID=`kkhVljGiMS` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_2.json`](../../evidence/claim_2.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "kkhVljGiMS",
    "claim_index": 2,
    "cpu_only": true,
    "domain": "claim-bound-structural",
    "title_hint": "On the Computational Complexity of Performative Prediction",
    "structured_mse": 0.0021553823437550955,
    "rel_param_err": 0.010261961825274245,
    "d": 4,
    "n": 200,
    "claim_numbers": [
      3.1,
      2.0,
      3.0,
      3.4
    ],
    "claim_keywords": [
      "ppad",
      "hardness",
      "persists",
      "simple",
      "setting",
      "loss",
      "quadratic",
      "distribution",
      "shift",
      "given",
      "affine",
      "equation"
    ],
    "claim_sha14": "1a7a1488233472",
    "claim_snippet": "This PPAD-hardness persists in the simple setting where the loss is quadratic, \u2113(x;z) = \u00bd||x\u2212z||\u00b2, and the distribution shift D(x) is given by an affine map g(x) (Section 3.1, Equation 2-3, Theorem 3.4)."
  },
  "domain": "claim-bound-structural",
  "orid": "kkhVljGiMS",
  "space_id": "neonforestmist/computational-complexity-performative-prediction-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:00:35.108658+00:00"
}