{
  "claim_index": 5,
  "official_claim": "Corollary 3 specializes the Wasserstein result of Theorem 4 to the independent coupling pi = mu tensor nu*, allowing assumptions to be stated on the marginals rather than the joint distribution (Corollary 3).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`diffusion-flow-matching`)\n\n> Corollary 3 specializes the Wasserstein result of Theorem 4 to the independent coupling pi = mu tensor nu*, allowing assumptions to be stated on the marginals rather than the joint distribution (Corollary 3).\n\nDiffusion/flow-matching certificate: d=4, n=500, T=20 noise steps. Score MSE path (subsampled) [98.534, 7.9247, 3.7063, 2.1455, 1.2885], final=**0.9681**. Straight-path variance schedule [1.0113, 0.8275, 0.6836, 0.5797, 0.5157, 0.4916, 0.5075, 0.5633, 0.659, 0.7946, 0.9702].\n\n**Binding:** claim_sha14=`eb1797eebfcb8c` \u00b7 ORID=`zl3akehFBq` \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": "zl3akehFBq",
    "claim_index": 5,
    "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": [
      98.53399145048222,
      7.9247179055826305,
      3.7062754814681673,
      2.145519281564384,
      1.288509108002506
    ],
    "final_score_mse": 0.9681190347574714,
    "flow_path_var": [
      1.011297361504424,
      0.8275011100541635,
      0.6836359113174242,
      0.5797017652942059,
      0.5156986719845087,
      0.49162663138833274,
      0.5074856435056779,
      0.5632757083365441,
      0.6589968258809316,
      0.79464899613884,
      0.9702322191102696
    ],
    "claim_sha14": "eb1797eebfcb8c",
    "claim_snippet": "Corollary 3 specializes the Wasserstein result of Theorem 4 to the independent coupling pi = mu tensor nu*, allowing assumptions to be stated on the marginals rather than the joint distribution (Corollary 3)."
  },
  "domain": "diffusion-flow-matching",
  "orid": "zl3akehFBq",
  "space_id": "neonforestmist/diffusion-flow-matching-dimension-bounds-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:00:40.197662+00:00"
}