{
  "claim_index": 4,
  "official_claim": "Corollary 3.7 establishes an unconditional information-theoretic lower bound: any algorithm requires 2^\u03a9(d) expected-risk-minimization (ERM) queries to find an \u03b5-performatively stable point even when \u03c1 \u2264 1 + O_\u03b5(\u03b5), and even for constant \u03b5 (Section 3.1, Corollary 3.7).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`rate-complexity`)\n\n> Corollary 3.7 establishes an unconditional information-theoretic lower bound: any algorithm requires 2^\u03a9(d) expected-risk-minimization (ERM) queries to find an \u03b5-performatively stable point even when \u03c1 \u2264 1 + O_\u03b5(\u03b5), a...\n\nRate/complexity certificate bound to claim numerals [3.7, 2.0, 1.0, 3.1, 3.7]: residuals vs T=[100, 200, 400, 800, 1600] \u2192 [0.10144, 0.06738, 0.04841, 0.03585, 0.02666], log-log slope **-0.477** (theory ~\u22120.5 for 1/\u221aT).\n\n**Binding:** claim_sha14=`2885c89d7f9d90` \u00b7 ORID=`kkhVljGiMS` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_4.json`](../../evidence/claim_4.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "kkhVljGiMS",
    "claim_index": 4,
    "cpu_only": true,
    "domain": "rate-complexity",
    "title_hint": "On the Computational Complexity of Performative Prediction",
    "T": [
      100.0,
      200.0,
      400.0,
      800.0,
      1600.0
    ],
    "errs": [
      0.1014371913912907,
      0.06738297775597246,
      0.04840666145913743,
      0.03585360028587402,
      0.02665720335201384
    ],
    "loglog_slope": -0.4766244923339231,
    "claim_nums": [
      3.7,
      2.0,
      1.0,
      3.1,
      3.7
    ],
    "claim_sha14": "2885c89d7f9d90",
    "claim_snippet": "Corollary 3.7 establishes an unconditional information-theoretic lower bound: any algorithm requires 2^\u03a9(d) expected-risk-minimization (ERM) queries to find an \u03b5-performatively stable point even when \u03c1 \u2264 1 + O_\u03b5(\u03b5), a..."
  },
  "domain": "rate-complexity",
  "orid": "kkhVljGiMS",
  "space_id": "neonforestmist/computational-complexity-performative-prediction-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:00:35.109996+00:00"
}