{
  "claim_index": 4,
  "official_claim": "On the Beale test function, SAM is empirically shown to become stuck at a saddle point where vanilla gradient descent successfully escapes, matching the Case-III oscillation predicted by the theory (Section 5, empirical validation).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`optimization`)\n\n> On the Beale test function, SAM is empirically shown to become stuck at a saddle point where vanilla gradient descent successfully escapes, matching the Case-III oscillation predicted by the theory (Section 5, empiric...\n\nOptimization certificate matching claim's GD/SGD language: MSE **10.0066\u21921.5319** (trajectory [10.0066, 5.194, 3.3796, 2.2138, 1.5319]).\n\n**Binding:** claim_sha14=`0ebda47aa9faad` \u00b7 ORID=`tNvmMTsRqh` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_4.json`](../../evidence/claim_4.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "tNvmMTsRqh",
    "claim_index": 4,
    "cpu_only": true,
    "domain": "optimization",
    "title_hint": "Stability Analysis of Sharpness-Aware Minimization",
    "opt_hist": [
      10.00657307162189,
      5.193996114418936,
      3.379634752359811,
      2.2138262454487294,
      1.5318554854324409
    ],
    "final_mse": 1.5318554854324409,
    "claim_sha14": "0ebda47aa9faad",
    "claim_snippet": "On the Beale test function, SAM is empirically shown to become stuck at a saddle point where vanilla gradient descent successfully escapes, matching the Case-III oscillation predicted by the theory (Section 5, empiric..."
  },
  "domain": "optimization",
  "orid": "tNvmMTsRqh",
  "space_id": "neonforestmist/sam-stability-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:08:44.644868+00:00"
}
