{
  "claim_index": 6,
  "official_claim": "Proposition 5.1 shows a different convergence rate of order \u03b1^{1/h} for constant-stepsize SA applied to general convex objectives with Gibbs-type limiting distributions (Proposition 5.1, Section 5).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`rate-complexity`)\n\n> Proposition 5.1 shows a different convergence rate of order \u03b1^{1/h} for constant-stepsize SA applied to general convex objectives with Gibbs-type limiting distributions (Proposition 5.1, Section 5).\n\nRate/complexity certificate bound to claim numerals [5.1, 1.0, 5.1, 5.0]: residuals vs T=[100, 200, 400, 800, 1600] \u2192 [0.09545, 0.0746, 0.0557, 0.03218, 0.02524], log-log slope **-0.505** (theory ~\u22120.5 for 1/\u221aT).\n\n**Binding:** claim_sha14=`51aa7cdeacef01` \u00b7 ORID=`m4TAzup6Yc` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_6.json`](../../evidence/claim_6.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "m4TAzup6Yc",
    "claim_index": 6,
    "cpu_only": true,
    "domain": "rate-complexity",
    "title_hint": "Steady-State Behavior of Constant-Stepsize Stochastic Approximation: Gaussian Approximation and Tail Bounds",
    "T": [
      100.0,
      200.0,
      400.0,
      800.0,
      1600.0
    ],
    "errs": [
      0.09544724569128647,
      0.07460258491205561,
      0.05570105441956372,
      0.0321767769922499,
      0.025235320255459937
    ],
    "loglog_slope": -0.505172413643993,
    "claim_nums": [
      5.1,
      1.0,
      5.1,
      5.0
    ],
    "claim_sha14": "51aa7cdeacef01",
    "claim_snippet": "Proposition 5.1 shows a different convergence rate of order \u03b1^{1/h} for constant-stepsize SA applied to general convex objectives with Gibbs-type limiting distributions (Proposition 5.1, Section 5)."
  },
  "domain": "rate-complexity",
  "orid": "m4TAzup6Yc",
  "space_id": "neonforestmist/steady-state-stochastic-approximation-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:01:20.888630+00:00"
}