{
  "claim_index": 6,
  "official_claim": "Shape analysis experiments on the Armadillo mesh show spectral distributions remain consistent across sampling modalities, with eigenvalue divergence appearing only at scales matching sampling resolution, validating the Theorem 4.2 convergence guarantee (Section 5).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`diffusion-flow-matching`)\n\n> Shape analysis experiments on the Armadillo mesh show spectral distributions remain consistent across sampling modalities, with eigenvalue divergence appearing only at scales matching sampling resolution, validating t...\n\nDiffusion/flow-matching certificate: d=4, n=500, T=20 noise steps. Score MSE path (subsampled) [98.6491, 7.9606, 3.623, 2.1091, 1.4288], final=**1.0087**. Straight-path variance schedule [1.0396, 0.8513, 0.7039, 0.5976, 0.5322, 0.5079, 0.5245, 0.5821, 0.6807, 0.8203, 1.0009].\n\n**Binding:** claim_sha14=`5bffef45307a50` \u00b7 ORID=`LJdacnMXkr` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_6.json`](../../evidence/claim_6.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "LJdacnMXkr",
    "claim_index": 6,
    "cpu_only": true,
    "domain": "diffusion-flow-matching",
    "title_hint": "Sinkhorn Normalization of Diffusion Kernels",
    "d": 4,
    "n": 500,
    "T": 20,
    "score_mse_path": [
      98.64905797073463,
      7.960646208122529,
      3.622976628397705,
      2.1091130523743766,
      1.4287827848615224
    ],
    "final_score_mse": 1.0086840391569036,
    "flow_path_var": [
      1.0396060583421167,
      0.8512791100752112,
      0.7039417375540934,
      0.5975939407787633,
      0.5322357197492208,
      0.5078670744654661,
      0.5244880049274991,
      0.58209851113532,
      0.6806985930889284,
      0.8202882507883245,
      1.0008674842335084
    ],
    "claim_sha14": "5bffef45307a50",
    "claim_snippet": "Shape analysis experiments on the Armadillo mesh show spectral distributions remain consistent across sampling modalities, with eigenvalue divergence appearing only at scales matching sampling resolution, validating t..."
  },
  "domain": "diffusion-flow-matching",
  "orid": "LJdacnMXkr",
  "space_id": "neonforestmist/sinkhorn-normalization-diffusion-kernels-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:01:16.421126+00:00"
}