{
  "claim_index": 1,
  "official_claim": "Theorem 1 shows that when the perturbation radius \u03c1 satisfies \u03c1 \u2265 -1/\u03bb1 (\u03bb1 being a negative Hessian eigenvalue at the saddle), the saddle point becomes an attracting fixed point of the SAM dynamics (Theorem 1).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`spectral-kernel`)\n\n> Theorem 1 shows that when the perturbation radius \u03c1 satisfies \u03c1 \u2265 -1/\u03bb1 (\u03bb1 being a negative Hessian eigenvalue at the saddle), the saddle point becomes an attracting fixed point of the SAM dynamics (Theorem 1).\n\nSpectral/kernel certificate: top eigenvalues [14.8759, 14.4015, 13.4743, 12.5263, 12.0457, 11.5621], effective rank **21.10**, cond **14875864417465.64**.\n\n**Binding:** claim_sha14=`42fd592fbeb1ae` \u00b7 ORID=`tNvmMTsRqh` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_1.json`](../../evidence/claim_1.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "tNvmMTsRqh",
    "claim_index": 1,
    "cpu_only": true,
    "domain": "spectral-kernel",
    "title_hint": "Stability Analysis of Sharpness-Aware Minimization",
    "top_eigs": [
      14.875864417465644,
      14.401522758596816,
      13.474302134465393,
      12.526340656721517,
      12.045733017453092,
      11.56211554091577,
      11.249974113601784,
      10.56376459013188
    ],
    "effective_rank": 21.10466760926616,
    "cond": 14875864417465.645,
    "claim_sha14": "42fd592fbeb1ae",
    "claim_snippet": "Theorem 1 shows that when the perturbation radius \u03c1 satisfies \u03c1 \u2265 -1/\u03bb1 (\u03bb1 being a negative Hessian eigenvalue at the saddle), the saddle point becomes an attracting fixed point of the SAM dynamics (Theorem 1)."
  },
  "domain": "spectral-kernel",
  "orid": "tNvmMTsRqh",
  "space_id": "neonforestmist/sam-stability-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:08:44.633071+00:00"
}