{
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  "official_claim": "Propositions 3.2 and 3.3 extend the same O(\u03b1^{1/2} log(1/\u03b1)) Wasserstein bound to linear stochastic approximation with a Hurwitz matrix and to contractive nonlinear stochastic approximation, respectively (Propositions 3.2 and 3.3, Section 3.2.2, Section 3.2.3).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`optimal-transport`)\n\n> Propositions 3.2 and 3.3 extend the same O(\u03b1^{1/2} log(1/\u03b1)) Wasserstein bound to linear stochastic approximation with a Hurwitz matrix and to contractive nonlinear stochastic approximation, respectively (Propositions...\n\nSinkhorn OT: cost **0.0356**, plan mass **1.000000**, m=24.\n\n**Binding:** claim_sha14=`a7faef1ba02533` \u00b7 ORID=`m4TAzup6Yc` \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",
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    "claim_index": 3,
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    "domain": "optimal-transport",
    "title_hint": "Steady-State Behavior of Constant-Stepsize Stochastic Approximation: Gaussian Approximation and Tail Bounds",
    "sinkhorn_cost": 0.03560786009275394,
    "mass": 0.9999999999752578,
    "m": 24,
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    "claim_snippet": "Propositions 3.2 and 3.3 extend the same O(\u03b1^{1/2} log(1/\u03b1)) Wasserstein bound to linear stochastic approximation with a Hurwitz matrix and to contractive nonlinear stochastic approximation, respectively (Propositions..."
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  "domain": "optimal-transport",
  "orid": "m4TAzup6Yc",
  "space_id": "neonforestmist/steady-state-stochastic-approximation-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:01:20.883977+00:00"
}