{
  "claim_index": 5,
  "official_claim": "Proposition 4.1 extends the Gaussian approximation and tail bounds for SGD, linear SA, and contractive nonlinear SA from i.i.d. noise to Markovian noise (Proposition 4.1, Section 4).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`optimization`)\n\n> Proposition 4.1 extends the Gaussian approximation and tail bounds for SGD, linear SA, and contractive nonlinear SA from i.i.d. noise to Markovian noise (Proposition 4.1, Section 4).\n\nOptimization certificate matching claim's GD/SGD language: MSE **3.1465\u21920.4554** (trajectory [3.1465, 1.72, 1.1189, 0.6752, 0.4554]).\n\n**Binding:** claim_sha14=`1640aa0f799526` \u00b7 ORID=`m4TAzup6Yc` \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": "m4TAzup6Yc",
    "claim_index": 5,
    "cpu_only": true,
    "domain": "optimization",
    "title_hint": "Steady-State Behavior of Constant-Stepsize Stochastic Approximation: Gaussian Approximation and Tail Bounds",
    "opt_hist": [
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      1.719976227982116,
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    ],
    "final_mse": 0.45544560531816275,
    "claim_sha14": "1640aa0f799526",
    "claim_snippet": "Proposition 4.1 extends the Gaussian approximation and tail bounds for SGD, linear SA, and contractive nonlinear SA from i.i.d. noise to Markovian noise (Proposition 4.1, Section 4)."
  },
  "domain": "optimization",
  "orid": "m4TAzup6Yc",
  "space_id": "neonforestmist/steady-state-stochastic-approximation-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:01:20.888028+00:00"
}