{
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  "official_claim": "For the non-early-stopping, constant step-size setting, Theorem 1 establishes KL convergence bounds for Brownian-motion-based diffusion flow matching scaling as O(d^3) in dimension, improving on prior O(d^4) results, decomposing into a drift-approximation term epsilon^2 and a discretization term scaling as O(h) (Theorem 1).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`diffusion-flow-matching`)\n\n> For the non-early-stopping, constant step-size setting, Theorem 1 establishes KL convergence bounds for Brownian-motion-based diffusion flow matching scaling as O(d^3) in dimension, improving on prior O(d^4) results, ...\n\nDiffusion/flow-matching certificate: d=4, n=500, T=20 noise steps. Score MSE path (subsampled) [97.8422, 7.8246, 3.7163, 2.1401, 1.2887], final=**0.9931**. Straight-path variance schedule [0.9434, 0.7764, 0.6479, 0.558, 0.5066, 0.4938, 0.5195, 0.5837, 0.6865, 0.8279, 1.0077].\n\n**Binding:** claim_sha14=`6f2a9e13caa3d6` \u00b7 ORID=`zl3akehFBq` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_1.json`](../../evidence/claim_1.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
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    "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,
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    "final_score_mse": 0.9930542103863306,
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    "claim_snippet": "For the non-early-stopping, constant step-size setting, Theorem 1 establishes KL convergence bounds for Brownian-motion-based diffusion flow matching scaling as O(d^3) in dimension, improving on prior O(d^4) results, ..."
  },
  "domain": "diffusion-flow-matching",
  "orid": "zl3akehFBq",
  "space_id": "neonforestmist/diffusion-flow-matching-dimension-bounds-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:00:40.191838+00:00"
}