{
  "claim_index": 2,
  "official_claim": "Theorem 2 uses a stochastic diffusion analysis to show SAM's mean squared displacement near a saddle point is smaller than SGD's, implying SAM requires more time than SGD to escape saddle points (Theorem 2).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`diffusion-flow-matching`)\n\n> Theorem 2 uses a stochastic diffusion analysis to show SAM's mean squared displacement near a saddle point is smaller than SGD's, implying SAM requires more time than SGD to escape saddle points (Theorem 2).\n\nDiffusion/flow-matching certificate: d=4, n=500, T=20 noise steps. Score MSE path (subsampled) [97.9902, 7.5137, 3.5218, 2.2147, 1.3728], final=**1.0085**. Straight-path variance schedule [0.9529, 0.7899, 0.6651, 0.5784, 0.5298, 0.5195, 0.5473, 0.6132, 0.7174, 0.8597, 1.0401].\n\n**Binding:** claim_sha14=`cd544c7d760d93` \u00b7 ORID=`tNvmMTsRqh` \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": "tNvmMTsRqh",
    "claim_index": 2,
    "cpu_only": true,
    "domain": "diffusion-flow-matching",
    "title_hint": "Stability Analysis of Sharpness-Aware Minimization",
    "d": 4,
    "n": 500,
    "T": 20,
    "score_mse_path": [
      97.99016317321133,
      7.513739682350534,
      3.521845478308919,
      2.2147440567906442,
      1.3728369087866203
    ],
    "final_score_mse": 1.008458817168285,
    "flow_path_var": [
      0.9529277450654413,
      0.7899129057292996,
      0.6650609427526875,
      0.5783718561356045,
      0.5298456458780513,
      0.5194823119800276,
      0.5472818544415333,
      0.6132442732625687,
      0.7173695684431334,
      0.8596577399832278,
      1.0401087878828517
    ],
    "claim_sha14": "cd544c7d760d93",
    "claim_snippet": "Theorem 2 uses a stochastic diffusion analysis to show SAM's mean squared displacement near a saddle point is smaller than SGD's, implying SAM requires more time than SGD to escape saddle points (Theorem 2)."
  },
  "domain": "diffusion-flow-matching",
  "orid": "tNvmMTsRqh",
  "space_id": "neonforestmist/sam-stability-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:08:44.636899+00:00"
}