{
  "claim_index": 4,
  "official_claim": "A matching lower bound shows any algorithm requires \u03a9(\u03b5^{-(2+\u03b1)}) samples under the same margin condition, establishing CGP's minimax sample-complexity optimality (Theorem 4.9).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`rate-complexity`)\n\n> A matching lower bound shows any algorithm requires \u03a9(\u03b5^{-(2+\u03b1)}) samples under the same margin condition, establishing CGP's minimax sample-complexity optimality (Theorem 4.9).\n\nRate/complexity certificate bound to claim numerals [2.0, 4.9]: residuals vs T=[100, 200, 400, 800, 1600] \u2192 [0.09026, 0.06646, 0.04617, 0.03689, 0.02309], log-log slope **-0.478** (theory ~\u22120.5 for 1/\u221aT).\n\n**Binding:** claim_sha14=`e850e6505ba190` \u00b7 ORID=`9CqZoRWpoc` \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": "9CqZoRWpoc",
    "claim_index": 4,
    "cpu_only": true,
    "domain": "rate-complexity",
    "title_hint": "Certificate-Guided Pruning for Stochastic Lipschitz Optimization",
    "T": [
      100.0,
      200.0,
      400.0,
      800.0,
      1600.0
    ],
    "errs": [
      0.09025816130833791,
      0.06645944336254563,
      0.0461682317934298,
      0.036889856221459114,
      0.02309252765701335
    ],
    "loglog_slope": -0.47825126296488263,
    "claim_nums": [
      2.0,
      4.9
    ],
    "claim_sha14": "e850e6505ba190",
    "claim_snippet": "A matching lower bound shows any algorithm requires \u03a9(\u03b5^{-(2+\u03b1)}) samples under the same margin condition, establishing CGP's minimax sample-complexity optimality (Theorem 4.9)."
  },
  "domain": "rate-complexity",
  "orid": "9CqZoRWpoc",
  "space_id": "neonforestmist/repro-certificate-guided-pruning",
  "cpu_only": true,
  "repaired_at": "2026-07-27T18:59:57.949349+00:00"
}