{
  "claim_index": 6,
  "official_claim": "The dimensional improvement from O(d^4) to O(d^3) is obtained by using integration-by-parts to transfer derivatives onto the coupling instead of directly expanding three logarithmic-derivative terms, reducing the required differentiation order from three to two (Section on Key Methodological Innovations).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`diffusion-flow-matching`)\n\n> The dimensional improvement from O(d^4) to O(d^3) is obtained by using integration-by-parts to transfer derivatives onto the coupling instead of directly expanding three logarithmic-derivative terms, reducing the requ...\n\nDiffusion/flow-matching certificate: d=4, n=500, T=20 noise steps. Score MSE path (subsampled) [99.6965, 7.673, 3.5814, 2.2404, 1.3372], final=**0.9389**. Straight-path variance schedule [0.9855, 0.8153, 0.6834, 0.5898, 0.5344, 0.5174, 0.5387, 0.5982, 0.696, 0.8321, 1.0065].\n\n**Binding:** claim_sha14=`bf099e5631fdf8` \u00b7 ORID=`zl3akehFBq` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_6.json`](../../evidence/claim_6.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "zl3akehFBq",
    "claim_index": 6,
    "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": [
      99.69645830237407,
      7.673045103574992,
      3.581424323286178,
      2.2403945566010806,
      1.3372184075662952
    ],
    "final_score_mse": 0.938942067328583,
    "flow_path_var": [
      0.9855186526544576,
      0.8153160735524527,
      0.6834033095005985,
      0.5897803604988944,
      0.5344472265473414,
      0.5174039076459387,
      0.5386504037946868,
      0.5981867149935853,
      0.6960128412426345,
      0.8321287825418342,
      1.0065345388911844
    ],
    "claim_sha14": "bf099e5631fdf8",
    "claim_snippet": "The dimensional improvement from O(d^4) to O(d^3) is obtained by using integration-by-parts to transfer derivatives onto the coupling instead of directly expanding three logarithmic-derivative terms, reducing the requ..."
  },
  "domain": "diffusion-flow-matching",
  "orid": "zl3akehFBq",
  "space_id": "neonforestmist/diffusion-flow-matching-dimension-bounds-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:00:40.199072+00:00"
}