{
  "claim_index": 1,
  "official_claim": "Theorem 3.1 (i.i.d. noise) and Theorem 4.1 (Markovian noise) bound the Wasserstein distance between the centered-scaled steady state Y^(\u03b1) = (X^(\u03b1) \u2212 x*)/\u221a\u03b1 and its Gaussian limit N(0, \u03a3_Y) by U\u221a\u03b1 log(1/\u03b1) (Theorems 3.1 and 4.1).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`optimal-transport`)\n\n> Theorem 3.1 (i.i.d. noise) and Theorem 4.1 (Markovian noise) bound the Wasserstein distance between the centered-scaled steady state Y^(\u03b1) = (X^(\u03b1) \u2212 x*)/\u221a\u03b1 and its Gaussian limit N(0, \u03a3_Y) by U\u221a\u03b1 log(1/\u03b1) (Theorems 3...\n\nSinkhorn OT: cost **0.0308**, plan mass **1.000000**, m=24.\n\n**Binding:** claim_sha14=`f22b2a67c583e1` \u00b7 ORID=`m4TAzup6Yc` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_1.json`](../../evidence/claim_1.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "m4TAzup6Yc",
    "claim_index": 1,
    "cpu_only": true,
    "domain": "optimal-transport",
    "title_hint": "Steady-State Behavior of Constant-Stepsize Stochastic Approximation: Gaussian Approximation and Tail Bounds",
    "sinkhorn_cost": 0.030758494359892592,
    "mass": 0.9999999999759822,
    "m": 24,
    "claim_sha14": "f22b2a67c583e1",
    "claim_snippet": "Theorem 3.1 (i.i.d. noise) and Theorem 4.1 (Markovian noise) bound the Wasserstein distance between the centered-scaled steady state Y^(\u03b1) = (X^(\u03b1) \u2212 x*)/\u221a\u03b1 and its Gaussian limit N(0, \u03a3_Y) by U\u221a\u03b1 log(1/\u03b1) (Theorems 3..."
  },
  "domain": "optimal-transport",
  "orid": "m4TAzup6Yc",
  "space_id": "neonforestmist/steady-state-stochastic-approximation-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:01:20.882435+00:00"
}