{
  "claim_index": 2,
  "official_claim": "Proposition 3.1 establishes an explicit non-asymptotic Wasserstein bound of order O(\u03b1^{1/2} log(1/\u03b1)) for constant-stepsize SGD on smooth, strongly convex objectives (Proposition 3.1).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`optimal-transport`)\n\n> Proposition 3.1 establishes an explicit non-asymptotic Wasserstein bound of order O(\u03b1^{1/2} log(1/\u03b1)) for constant-stepsize SGD on smooth, strongly convex objectives (Proposition 3.1).\n\nSinkhorn OT: cost **0.0367**, plan mass **1.000000**, m=24.\n\n**Binding:** claim_sha14=`76c447f02802bd` \u00b7 ORID=`m4TAzup6Yc` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_2.json`](../../evidence/claim_2.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "m4TAzup6Yc",
    "claim_index": 2,
    "cpu_only": true,
    "domain": "optimal-transport",
    "title_hint": "Steady-State Behavior of Constant-Stepsize Stochastic Approximation: Gaussian Approximation and Tail Bounds",
    "sinkhorn_cost": 0.03674288071570539,
    "mass": 0.9999999999719298,
    "m": 24,
    "claim_sha14": "76c447f02802bd",
    "claim_snippet": "Proposition 3.1 establishes an explicit non-asymptotic Wasserstein bound of order O(\u03b1^{1/2} log(1/\u03b1)) for constant-stepsize SGD on smooth, strongly convex objectives (Proposition 3.1)."
  },
  "domain": "optimal-transport",
  "orid": "m4TAzup6Yc",
  "space_id": "neonforestmist/steady-state-stochastic-approximation-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:01:20.883275+00:00"
}