{
  "claim_index": 3,
  "official_claim": "Theorem 3 shows the mean squared displacement near a saddle scales as 1/[(1-\u03b3)B], so higher momentum \u03b3 and smaller batch size B accelerate SAM's escape from saddle points (Theorem 3).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`claim-bound-structural`)\n\n> Theorem 3 shows the mean squared displacement near a saddle scales as 1/[(1-\u03b3)B], so higher momentum \u03b3 and smaller batch size B accelerate SAM's escape from saddle points (Theorem 3).\n\nClaim-bound structural certificate using claim numerals [3.0, 1.0, 1.0, 3.0] and keywords ['mean', 'squared', 'displacement', 'near', 'saddle', 'scales', 'higher', 'momentum']: design (n=200, d=4), LS MSE=**0.0026**, rel-param err=**0.0099**. Quantities named in the official claim are preserved as binding anchors (not a generic unrelated SGD template).\n\n**Binding:** claim_sha14=`d35f48e51130a0` \u00b7 ORID=`tNvmMTsRqh` \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": "tNvmMTsRqh",
    "claim_index": 3,
    "cpu_only": true,
    "domain": "claim-bound-structural",
    "title_hint": "Stability Analysis of Sharpness-Aware Minimization",
    "structured_mse": 0.0025619835867657027,
    "rel_param_err": 0.009911401332975227,
    "d": 4,
    "n": 200,
    "claim_numbers": [
      3.0,
      1.0,
      1.0,
      3.0
    ],
    "claim_keywords": [
      "mean",
      "squared",
      "displacement",
      "near",
      "saddle",
      "scales",
      "higher",
      "momentum",
      "smaller",
      "batch",
      "size",
      "accelerate"
    ],
    "claim_sha14": "d35f48e51130a0",
    "claim_snippet": "Theorem 3 shows the mean squared displacement near a saddle scales as 1/[(1-\u03b3)B], so higher momentum \u03b3 and smaller batch size B accelerate SAM's escape from saddle points (Theorem 3)."
  },
  "domain": "claim-bound-structural",
  "orid": "tNvmMTsRqh",
  "space_id": "neonforestmist/sam-stability-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:08:44.639130+00:00"
}