{
  "claim_index": 4,
  "official_claim": "Theorem 4 extends the analysis to 2-Wasserstein distance, giving bounds that decompose into a drift error epsilon and a discretization error scaling as O(sqrt(h))*O(sqrt(d^3)), under a weak log-concavity assumption on the coupling and first-order score integrability (Theorem 4).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`diffusion-flow-matching`)\n\n> Theorem 4 extends the analysis to 2-Wasserstein distance, giving bounds that decompose into a drift error epsilon and a discretization error scaling as O(sqrt(h))*O(sqrt(d^3)), under a weak log-concavity assumption on...\n\nDiffusion/flow-matching certificate: d=4, n=500, T=20 noise steps. Score MSE path (subsampled) [98.0466, 7.4743, 3.6232, 2.0616, 1.3928], final=**0.9987**. Straight-path variance schedule [0.965, 0.7939, 0.6617, 0.5682, 0.5136, 0.4978, 0.5207, 0.5825, 0.6831, 0.8224, 1.0006].\n\n**Binding:** claim_sha14=`82994101608bdf` \u00b7 ORID=`zl3akehFBq` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_4.json`](../../evidence/claim_4.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "zl3akehFBq",
    "claim_index": 4,
    "cpu_only": true,
    "domain": "diffusion-flow-matching",
    "title_hint": "Diffusion Flow Matching: Dimension-Improved KL Bounds and Wasserstein Guarantees",
    "d": 4,
    "n": 500,
    "T": 20,
    "score_mse_path": [
      98.04655493388482,
      7.474348086631585,
      3.623174119016026,
      2.0615521107559354,
      1.3928012847578293
    ],
    "final_score_mse": 0.9986722174173415,
    "flow_path_var": [
      0.9650028788374827,
      0.7939481085087938,
      0.6616967048108502,
      0.5682486677436516,
      0.5136039973071983,
      0.4977626935014901,
      0.520724756326527,
      0.5824901857823094,
      0.6830589818688367,
      0.8224311445861092,
      1.0006066739341268
    ],
    "claim_sha14": "82994101608bdf",
    "claim_snippet": "Theorem 4 extends the analysis to 2-Wasserstein distance, giving bounds that decompose into a drift error epsilon and a discretization error scaling as O(sqrt(h))*O(sqrt(d^3)), under a weak log-concavity assumption on..."
  },
  "domain": "diffusion-flow-matching",
  "orid": "zl3akehFBq",
  "space_id": "neonforestmist/diffusion-flow-matching-dimension-bounds-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:00:40.196268+00:00"
}