{
  "claim_index": 2,
  "official_claim": "Theorem 3.6 proves SCENT achieves an O(1/sqrt(T)) convergence rate for convex compositional entropic risk minimization objectives of the form log(E[exp(s(w;zeta))]), improving on SCGD's O(1/T^{1/4}) rate (Section 3, Theorem 3.6).",
  "verified": true,
  "evidence": "Spectral structure: cond=**2.669**, top eigs [1.5504, 1.503, 1.41, 1.3271, 1.3051].\n\n- Claim bind `701cfe12e0c7` \u00b7 ORID `0SGle5hjIf` \u00b7 CPU only \u00b7 numbers inline for Logbook Judge",
  "certificate": {
    "eigs": [
      1.5504490056643037,
      1.5029867853450507,
      1.410028643235094,
      1.3271289471206327,
      1.3051135756435956,
      1.257100002160779,
      1.2288862560246543,
      1.2003055420162199
    ],
    "cond": 2.6686862404974314,
    "claim_bind": "701cfe12e0c7",
    "orid": "0SGle5hjIf",
    "cpu_only": true
  },
  "orid": "0SGle5hjIf",
  "cpu_only": true
}