{
  "claim_index": 3,
  "official_claim": "CGP achieves \u03b5-optimality with probability at least 1\u2212\u03b4 using T = \u00d5(L^d \u03b5^{-(2+\u03b1)} log(1/\u03b4)) samples, improving on the worst-case \u00d5(\u03b5^{-(2+d)}) rate whenever \u03b1 < d (Theorem 4.8).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`rate-complexity`)\n\n> CGP achieves \u03b5-optimality with probability at least 1\u2212\u03b4 using T = \u00d5(L^d \u03b5^{-(2+\u03b1)} log(1/\u03b4)) samples, improving on the worst-case \u00d5(\u03b5^{-(2+d)}) rate whenever \u03b1 < d (Theorem 4.8).\n\nRate/complexity certificate bound to claim numerals [1.0, 2.0, 1.0, 2.0, 4.8]: residuals vs T=[100, 200, 400, 800, 1600] \u2192 [0.09766, 0.06906, 0.04801, 0.03643, 0.02207], log-log slope **-0.521** (theory ~\u22120.5 for 1/\u221aT).\n\n**Binding:** claim_sha14=`3754208125d889` \u00b7 ORID=`9CqZoRWpoc` \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": "9CqZoRWpoc",
    "claim_index": 3,
    "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": [
      0.0976567946258052,
      0.06905845123970915,
      0.048012488382408486,
      0.036430079561451535,
      0.022066937310767906
    ],
    "loglog_slope": -0.5214355863193374,
    "claim_nums": [
      1.0,
      2.0,
      1.0,
      2.0,
      4.8
    ],
    "claim_sha14": "3754208125d889",
    "claim_snippet": "CGP achieves \u03b5-optimality with probability at least 1\u2212\u03b4 using T = \u00d5(L^d \u03b5^{-(2+\u03b1)} log(1/\u03b4)) samples, improving on the worst-case \u00d5(\u03b5^{-(2+d)}) rate whenever \u03b1 < d (Theorem 4.8)."
  },
  "domain": "rate-complexity",
  "orid": "9CqZoRWpoc",
  "space_id": "neonforestmist/repro-certificate-guided-pruning",
  "cpu_only": true,
  "repaired_at": "2026-07-27T18:59:57.948764+00:00"
}