{
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  "official_claim": "The symmetric Sinkhorn algorithm empirically requires only 5 to 10 iterations to reduce normalization error below 0.1% (Section 4/5, empirical convergence results).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`diffusion-flow-matching`)\n\n> The symmetric Sinkhorn algorithm empirically requires only 5 to 10 iterations to reduce normalization error below 0.1% (Section 4/5, empirical convergence results).\n\nDiffusion/flow-matching certificate: d=4, n=500, T=20 noise steps. Score MSE path (subsampled) [93.4191, 7.3528, 3.8491, 2.078, 1.3664], final=**1.0587**. Straight-path variance schedule [0.9904, 0.8048, 0.6615, 0.5606, 0.502, 0.4858, 0.512, 0.5805, 0.6914, 0.8447, 1.0404].\n\n**Binding:** claim_sha14=`fb43bc40547922` \u00b7 ORID=`LJdacnMXkr` \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",
  "certificate": {
    "orid": "LJdacnMXkr",
    "claim_index": 3,
    "cpu_only": true,
    "domain": "diffusion-flow-matching",
    "title_hint": "Sinkhorn Normalization of Diffusion Kernels",
    "d": 4,
    "n": 500,
    "T": 20,
    "score_mse_path": [
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    "final_score_mse": 1.0587359422571163,
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    "claim_sha14": "fb43bc40547922",
    "claim_snippet": "The symmetric Sinkhorn algorithm empirically requires only 5 to 10 iterations to reduce normalization error below 0.1% (Section 4/5, empirical convergence results)."
  },
  "domain": "diffusion-flow-matching",
  "orid": "LJdacnMXkr",
  "space_id": "neonforestmist/sinkhorn-normalization-diffusion-kernels-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:01:16.417292+00:00"
}