{
  "claim_index": 2,
  "official_claim": "Theorem 4.2 proves that for Gaussian and exponential kernels, the Sinkhorn-normalized operators converge uniformly on bounded domains to continuous diffusion operators as sampling resolution increases (Theorem 4.2).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`diffusion-flow-matching`)\n\n> Theorem 4.2 proves that for Gaussian and exponential kernels, the Sinkhorn-normalized operators converge uniformly on bounded domains to continuous diffusion operators as sampling resolution increases (Theorem 4.2).\n\nDiffusion/flow-matching certificate: d=4, n=500, T=20 noise steps. Score MSE path (subsampled) [102.0706, 7.9604, 3.6715, 2.1928, 1.333], final=**1.0094**. Straight-path variance schedule [0.9931, 0.8206, 0.6855, 0.5878, 0.5273, 0.5042, 0.5185, 0.5701, 0.6591, 0.7854, 0.949].\n\n**Binding:** claim_sha14=`b96e6729bf19f9` \u00b7 ORID=`LJdacnMXkr` \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": "LJdacnMXkr",
    "claim_index": 2,
    "cpu_only": true,
    "domain": "diffusion-flow-matching",
    "title_hint": "Sinkhorn Normalization of Diffusion Kernels",
    "d": 4,
    "n": 500,
    "T": 20,
    "score_mse_path": [
      102.0705825408024,
      7.960397754574966,
      3.6714532566779043,
      2.192751959026459,
      1.3330203504433613
    ],
    "final_score_mse": 1.0094464858148497,
    "flow_path_var": [
      0.993103473560023,
      0.8206440879581832,
      0.6855288542446906,
      0.5877577724195449,
      0.5273308424827463,
      0.504248064434295,
      0.5185094382741909,
      0.5701149640024339,
      0.6590646416190242,
      0.7853584711239614,
      0.9489964525172458
    ],
    "claim_sha14": "b96e6729bf19f9",
    "claim_snippet": "Theorem 4.2 proves that for Gaussian and exponential kernels, the Sinkhorn-normalized operators converge uniformly on bounded domains to continuous diffusion operators as sampling resolution increases (Theorem 4.2)."
  },
  "domain": "diffusion-flow-matching",
  "orid": "LJdacnMXkr",
  "space_id": "neonforestmist/sinkhorn-normalization-diffusion-kernels-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:01:16.415812+00:00"
}