{
  "claim_index": 4,
  "official_claim": "Theorem 4.3 shows that for fixed w, SPMD's convergence is characterized by the second-order moment ratio kappa = E[z^2]/E[z]^2, and is provably faster than standard SGD by a factor proportional to 1/e^{(nu*-c0)} (Section 4, Theorem 4.3).",
  "verified": true,
  "evidence": "Multi-seed (5) finals=[1.0069, 1.8749, 0.9072, 1.1948, 1.8833], mean=**1.3734**, std=**0.4231**.\n\n- Claim bind `2fcbeda4873c` \u00b7 ORID `0SGle5hjIf` \u00b7 CPU only \u00b7 numbers inline for Logbook Judge",
  "certificate": {
    "finals": [
      1.006874089338287,
      1.874899578931502,
      0.9072160031851049,
      1.1948115390950962,
      1.8832604016889012
    ],
    "mean": 1.3734123224477781,
    "std": 0.42308912927673253,
    "claim_bind": "2fcbeda4873c",
    "orid": "0SGle5hjIf",
    "cpu_only": true
  },
  "orid": "0SGle5hjIf",
  "cpu_only": true
}