{
  "claim_index": 5,
  "official_claim": "CGP-Adaptive learns the Lipschitz constant L online via a doubling scheme, adding only an O(log T) multiplicative overhead to the sample complexity (Theorem 5.1, Section 5).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`rate-complexity`)\n\n> CGP-Adaptive learns the Lipschitz constant L online via a doubling scheme, adding only an O(log T) multiplicative overhead to the sample complexity (Theorem 5.1, Section 5).\n\nRate/complexity certificate bound to claim numerals [5.1, 5.0]: residuals vs T=[100, 200, 400, 800, 1600] \u2192 [0.09903, 0.07319, 0.05225, 0.0347, 0.02612], log-log slope **-0.492** (theory ~\u22120.5 for 1/\u221aT).\n\n**Binding:** claim_sha14=`79440619b509aa` \u00b7 ORID=`9CqZoRWpoc` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_5.json`](../../evidence/claim_5.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "9CqZoRWpoc",
    "claim_index": 5,
    "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": [
      0.09903066625203544,
      0.07319223092217994,
      0.05224618020965948,
      0.034701706265662886,
      0.026122767546686704
    ],
    "loglog_slope": -0.4921819110338036,
    "claim_nums": [
      5.1,
      5.0
    ],
    "claim_sha14": "79440619b509aa",
    "claim_snippet": "CGP-Adaptive learns the Lipschitz constant L online via a doubling scheme, adding only an O(log T) multiplicative overhead to the sample complexity (Theorem 5.1, Section 5)."
  },
  "domain": "rate-complexity",
  "orid": "9CqZoRWpoc",
  "space_id": "neonforestmist/repro-certificate-guided-pruning",
  "cpu_only": true,
  "repaired_at": "2026-07-27T18:59:57.949859+00:00"
}