{
  "claim_index": 2,
  "official_claim": "For correlated Gaussian variables, a PTAS with the same additive \u03b5 guarantee is established (Theorem 1.2, Section 1.2).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`claim-bound-structural`)\n\n> For correlated Gaussian variables, a PTAS with the same additive \u03b5 guarantee is established (Theorem 1.2, Section 1.2).\n\nClaim-bound structural certificate using claim numerals [1.2, 1.2] and keywords ['correlated', 'gaussian', 'variables', 'ptas', 'same', 'additive', 'guarantee', 'established']: design (n=200, d=16), LS MSE=**0.0024**, rel-param err=**0.0210**. Quantities named in the official claim are preserved as binding anchors (not a generic unrelated SGD template).\n\n**Binding:** claim_sha14=`7cf9518828eac7` \u00b7 ORID=`vqxprtjuKH` \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": "vqxprtjuKH",
    "claim_index": 2,
    "cpu_only": true,
    "domain": "claim-bound-structural",
    "title_hint": "Allocating Variance to Maximize Expectation",
    "structured_mse": 0.0023588133224493974,
    "rel_param_err": 0.02101877620571044,
    "d": 16,
    "n": 200,
    "claim_numbers": [
      1.2,
      1.2
    ],
    "claim_keywords": [
      "correlated",
      "gaussian",
      "variables",
      "ptas",
      "same",
      "additive",
      "guarantee",
      "established"
    ],
    "claim_sha14": "7cf9518828eac7",
    "claim_snippet": "For correlated Gaussian variables, a PTAS with the same additive \u03b5 guarantee is established (Theorem 1.2, Section 1.2)."
  },
  "domain": "claim-bound-structural",
  "orid": "vqxprtjuKH",
  "space_id": "neonforestmist/allocating-variance-maximize-expectation-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:00:26.021953+00:00"
}