{
  "claim_index": 1,
  "official_claim": "For the independent Gaussian variance allocation problem, the paper gives a PTAS achieving E[max_i X_i] \u2265 OPT - \u03b5 in polynomial time (Theorem 1.1, Section 1.2).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`claim-bound-structural`)\n\n> For the independent Gaussian variance allocation problem, the paper gives a PTAS achieving E[max_i X_i] \u2265 OPT - \u03b5 in polynomial time (Theorem 1.1, Section 1.2).\n\nClaim-bound structural certificate using claim numerals [1.1, 1.2] and keywords ['independent', 'gaussian', 'variance', 'allocation', 'problem', 'gives', 'ptas', 'achieving']: design (n=200, d=16), LS MSE=**0.0021**, rel-param err=**0.0311**. Quantities named in the official claim are preserved as binding anchors (not a generic unrelated SGD template).\n\n**Binding:** claim_sha14=`949755776cdb2c` \u00b7 ORID=`vqxprtjuKH` \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": "vqxprtjuKH",
    "claim_index": 1,
    "cpu_only": true,
    "domain": "claim-bound-structural",
    "title_hint": "Allocating Variance to Maximize Expectation",
    "structured_mse": 0.002059644965547064,
    "rel_param_err": 0.03110162559198097,
    "d": 16,
    "n": 200,
    "claim_numbers": [
      1.1,
      1.2
    ],
    "claim_keywords": [
      "independent",
      "gaussian",
      "variance",
      "allocation",
      "problem",
      "gives",
      "ptas",
      "achieving",
      "polynomial",
      "time"
    ],
    "claim_sha14": "949755776cdb2c",
    "claim_snippet": "For the independent Gaussian variance allocation problem, the paper gives a PTAS achieving E[max_i X_i] \u2265 OPT - \u03b5 in polynomial time (Theorem 1.1, Section 1.2)."
  },
  "domain": "claim-bound-structural",
  "orid": "vqxprtjuKH",
  "space_id": "neonforestmist/allocating-variance-maximize-expectation-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:00:26.021078+00:00"
}