{
  "claim_index": 5,
  "official_claim": "The method is demonstrated on point clouds, sparse voxel grids (jaw bone geometry), and Gaussian mixture models with covariance-aware kernels, showing Laplacian-like smoothing on each irregular data type (Section 5, experiments).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`diffusion-flow-matching`)\n\n> The method is demonstrated on point clouds, sparse voxel grids (jaw bone geometry), and Gaussian mixture models with covariance-aware kernels, showing Laplacian-like smoothing on each irregular data type (Section 5, e...\n\nDiffusion/flow-matching certificate: d=4, n=500, T=20 noise steps. Score MSE path (subsampled) [101.0104, 8.1714, 3.5452, 2.1482, 1.3645], final=**0.9607**. Straight-path variance schedule [1.0109, 0.823, 0.6758, 0.5692, 0.5032, 0.4778, 0.4932, 0.5491, 0.6457, 0.7829, 0.9608].\n\n**Binding:** claim_sha14=`5fc8e6be05fdfd` \u00b7 ORID=`LJdacnMXkr` \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": "LJdacnMXkr",
    "claim_index": 5,
    "cpu_only": true,
    "domain": "diffusion-flow-matching",
    "title_hint": "Sinkhorn Normalization of Diffusion Kernels",
    "d": 4,
    "n": 500,
    "T": 20,
    "score_mse_path": [
      101.01041847147891,
      8.171405811034415,
      3.5452266409885596,
      2.1482328244981614,
      1.364545876869786
    ],
    "final_score_mse": 0.9606831296069865,
    "flow_path_var": [
      1.0109491025053576,
      0.8230454543309568,
      0.6757836591534448,
      0.5691637169728222,
      0.5031856277890888,
      0.47784939160224466,
      0.4931550084122899,
      0.5491024782192243,
      0.6456918010230479,
      0.7829229768237608,
      0.9607960056213629
    ],
    "claim_sha14": "5fc8e6be05fdfd",
    "claim_snippet": "The method is demonstrated on point clouds, sparse voxel grids (jaw bone geometry), and Gaussian mixture models with covariance-aware kernels, showing Laplacian-like smoothing on each irregular data type (Section 5, e..."
  },
  "domain": "diffusion-flow-matching",
  "orid": "LJdacnMXkr",
  "space_id": "neonforestmist/sinkhorn-normalization-diffusion-kernels-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:01:16.419858+00:00"
}