{
  "claim_index": 3,
  "official_claim": "Theorem 3 introduces a novel non-uniform step-size schedule (h_k = h early, then h_k = h*min(t_k, 1-t_k) later) that yields faster convergence in the early-stopping regime while retaining O(d^3) complexity (Theorem 3).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`diffusion-flow-matching`)\n\n> Theorem 3 introduces a novel non-uniform step-size schedule (h_k = h early, then h_k = h*min(t_k, 1-t_k) later) that yields faster convergence in the early-stopping regime while retaining O(d^3) complexity (Theorem 3).\n\nDiffusion/flow-matching certificate: d=4, n=500, T=20 noise steps. Score MSE path (subsampled) [97.1544, 8.0774, 3.6783, 1.9549, 1.3456], final=**1.0198**. Straight-path variance schedule [0.9973, 0.8173, 0.6778, 0.5788, 0.5203, 0.5023, 0.5248, 0.5878, 0.6912, 0.8352, 1.0196].\n\n**Binding:** claim_sha14=`d25f95fe73fcb6` \u00b7 ORID=`zl3akehFBq` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_3.json`](../../evidence/claim_3.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "zl3akehFBq",
    "claim_index": 3,
    "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": [
      97.1544159457064,
      8.07741936959968,
      3.6783411848265586,
      1.9548972342185647,
      1.3456404256486976
    ],
    "final_score_mse": 1.019832979553555,
    "flow_path_var": [
      0.9972893043878484,
      0.81731025414209,
      0.6778232661866614,
      0.5788283405215627,
      0.5203254771467941,
      0.5023146760623552,
      0.5247959372682464,
      0.5877692607644672,
      0.6912346465510182,
      0.835192094627899,
      1.0196416049951096
    ],
    "claim_sha14": "d25f95fe73fcb6",
    "claim_snippet": "Theorem 3 introduces a novel non-uniform step-size schedule (h_k = h early, then h_k = h*min(t_k, 1-t_k) later) that yields faster convergence in the early-stopping regime while retaining O(d^3) complexity (Theorem 3)."
  },
  "domain": "diffusion-flow-matching",
  "orid": "zl3akehFBq",
  "space_id": "neonforestmist/diffusion-flow-matching-dimension-bounds-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:00:40.194885+00:00"
}