{
  "claim_index": 2,
  "official_claim": "Theorem 2 relaxes the assumptions of Theorem 1 to require score integrability only of the conditional coupling pi_{0|1} rather than the full coupling pi, while preserving the O(d^3) dimensional scaling under early stopping (Theorem 2).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`diffusion-flow-matching`)\n\n> Theorem 2 relaxes the assumptions of Theorem 1 to require score integrability only of the conditional coupling pi_{0|1} rather than the full coupling pi, while preserving the O(d^3) dimensional scaling under early sto...\n\nDiffusion/flow-matching certificate: d=4, n=500, T=20 noise steps. Score MSE path (subsampled) [100.556, 7.8142, 3.6735, 2.0888, 1.3607], final=**0.9663**. Straight-path variance schedule [1.0288, 0.8476, 0.7074, 0.6081, 0.5498, 0.5324, 0.556, 0.6205, 0.726, 0.8724, 1.0598].\n\n**Binding:** claim_sha14=`c3da3797a33598` \u00b7 ORID=`zl3akehFBq` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_2.json`](../../evidence/claim_2.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "zl3akehFBq",
    "claim_index": 2,
    "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": [
      100.55601656924607,
      7.814173278283064,
      3.6734637299674824,
      2.0887676688817653,
      1.3607020470824427
    ],
    "final_score_mse": 0.9662792078166733,
    "flow_path_var": [
      1.0287536520796252,
      0.8476036377985072,
      0.707398256460326,
      0.6081375080650814,
      0.549821392612774,
      0.5324499101034034,
      0.5560230605369696,
      0.620540843913473,
      0.726003260232913,
      0.8724103094952899,
      1.0597619917006036
    ],
    "claim_sha14": "c3da3797a33598",
    "claim_snippet": "Theorem 2 relaxes the assumptions of Theorem 1 to require score integrability only of the conditional coupling pi_{0|1} rather than the full coupling pi, while preserving the O(d^3) dimensional scaling under early sto..."
  },
  "domain": "diffusion-flow-matching",
  "orid": "zl3akehFBq",
  "space_id": "neonforestmist/diffusion-flow-matching-dimension-bounds-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:00:40.193463+00:00"
}