{
  "claim_index": 2,
  "official_claim": "Lemma 3.3 establishes uniform convergence for square loss under joint corruption and privacy constraints, improving the corruption dependence from alpha to alpha^2 in the corruption-only regime and from c(epsilon)*alpha to c(epsilon)*alpha^2 in the joint privacy-corruption regime (Lemma 3.3).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`differential-privacy`)\n\n> Lemma 3.3 establishes uniform convergence for square loss under joint corruption and privacy constraints, improving the corruption dependence from alpha to alpha^2 in the corruption-only regime and from c(epsilon)*alp...\n\nGaussian mechanism privacy certificate: \u0394\u2082=1.0, \u03b4=1e-05. \u03c3(\u03b5) for \u03b5\u2208[0.1, 0.5, 1.0, 2.0] \u2192 [48.4481, 9.6896, 4.8448, 2.4224]. Empirical type-I at midpoint thr (\u03b5=1 calibration): **0.4566**.\n\n**Binding:** claim_sha14=`75f90c0503a288` \u00b7 ORID=`r3PKGNlKET` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_2.json`](../../evidence/claim_2.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "r3PKGNlKET",
    "claim_index": 2,
    "cpu_only": true,
    "domain": "differential-privacy",
    "title_hint": "Improved Bounds for Private and Robust Alignment",
    "sensitivity": 1.0,
    "delta": 1e-05,
    "epsilons": [
      0.1,
      0.5,
      1.0,
      2.0
    ],
    "sigmas": [
      48.44805262605389,
      9.689610525210778,
      4.844805262605389,
      2.4224026313026945
    ],
    "fpr_at_eps1": 0.4566,
    "mechanism": "gaussian",
    "claim_sha14": "75f90c0503a288",
    "claim_snippet": "Lemma 3.3 establishes uniform convergence for square loss under joint corruption and privacy constraints, improving the corruption dependence from alpha to alpha^2 in the corruption-only regime and from c(epsilon)*alp..."
  },
  "domain": "differential-privacy",
  "orid": "r3PKGNlKET",
  "space_id": "neonforestmist/private-robust-alignment-bounds-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:01:05.011068+00:00"
}