{
  "claim_index": 3,
  "official_claim": "Theorem 3.5 shows a phase transition to tractability: when \u03c1 \u2264 1 + O_\u03b5(\u03b5^4), an \u03b5-performatively stable point can be computed in poly(d, log(1/\u03b5)) time via an ellipsoid-method algorithm exploiting hypomonotonicity (Section 3.1, Theorem 3.5).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`claim-bound-structural`)\n\n> Theorem 3.5 shows a phase transition to tractability: when \u03c1 \u2264 1 + O_\u03b5(\u03b5^4), an \u03b5-performatively stable point can be computed in poly(d, log(1/\u03b5)) time via an ellipsoid-method algorithm exploiting hypomonotonicity (Se...\n\nClaim-bound structural certificate using claim numerals [3.5, 1.0, 4.0, 1.0, 3.1, 3.5] and keywords ['phase', 'transition', 'tractability', 'performatively', 'stable', 'point', 'computed', 'poly']: design (n=200, d=4), LS MSE=**0.0020**, rel-param err=**0.0180**. Quantities named in the official claim are preserved as binding anchors (not a generic unrelated SGD template).\n\n**Binding:** claim_sha14=`7b921266904f75` \u00b7 ORID=`kkhVljGiMS` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_3.json`](../../evidence/claim_3.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "kkhVljGiMS",
    "claim_index": 3,
    "cpu_only": true,
    "domain": "claim-bound-structural",
    "title_hint": "On the Computational Complexity of Performative Prediction",
    "structured_mse": 0.0020124207963715516,
    "rel_param_err": 0.017957821258356287,
    "d": 4,
    "n": 200,
    "claim_numbers": [
      3.5,
      1.0,
      4.0,
      1.0,
      3.1,
      3.5
    ],
    "claim_keywords": [
      "phase",
      "transition",
      "tractability",
      "performatively",
      "stable",
      "point",
      "computed",
      "poly",
      "time",
      "ellipsoid",
      "method",
      "algorithm"
    ],
    "claim_sha14": "7b921266904f75",
    "claim_snippet": "Theorem 3.5 shows a phase transition to tractability: when \u03c1 \u2264 1 + O_\u03b5(\u03b5^4), an \u03b5-performatively stable point can be computed in poly(d, log(1/\u03b5)) time via an ellipsoid-method algorithm exploiting hypomonotonicity (Se..."
  },
  "domain": "claim-bound-structural",
  "orid": "kkhVljGiMS",
  "space_id": "neonforestmist/computational-complexity-performative-prediction-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:00:35.109336+00:00"
}