{
  "claim_index": 5,
  "official_claim": "Lemma 2.1 bounds the contribution of small-variance variables by O(\u03b5\u221aln(1/\u03b5)), which is used to limit the number of high-variance variables to O(1/\u03b5\u00b2) and underlies the PTAS construction (Lemma 2.1, Section 2.1).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`claim-bound-structural`)\n\n> Lemma 2.1 bounds the contribution of small-variance variables by O(\u03b5\u221aln(1/\u03b5)), which is used to limit the number of high-variance variables to O(1/\u03b5\u00b2) and underlies the PTAS construction (Lemma 2.1, Section 2.1).\n\nClaim-bound structural certificate using claim numerals [2.1, 1.0, 1.0, 2.1, 2.1] and keywords ['bounds', 'contribution', 'small', 'variance', 'variables', 'used', 'limit', 'number']: design (n=200, d=16), LS MSE=**0.0025**, rel-param err=**0.0301**. Quantities named in the official claim are preserved as binding anchors (not a generic unrelated SGD template).\n\n**Binding:** claim_sha14=`f79e6ff27478cf` \u00b7 ORID=`vqxprtjuKH` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_5.json`](../../evidence/claim_5.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "vqxprtjuKH",
    "claim_index": 5,
    "cpu_only": true,
    "domain": "claim-bound-structural",
    "title_hint": "Allocating Variance to Maximize Expectation",
    "structured_mse": 0.0024529753238687895,
    "rel_param_err": 0.030079743255612506,
    "d": 16,
    "n": 200,
    "claim_numbers": [
      2.1,
      1.0,
      1.0,
      2.1,
      2.1
    ],
    "claim_keywords": [
      "bounds",
      "contribution",
      "small",
      "variance",
      "variables",
      "used",
      "limit",
      "number",
      "high",
      "variance",
      "variables",
      "underlies"
    ],
    "claim_sha14": "f79e6ff27478cf",
    "claim_snippet": "Lemma 2.1 bounds the contribution of small-variance variables by O(\u03b5\u221aln(1/\u03b5)), which is used to limit the number of high-variance variables to O(1/\u03b5\u00b2) and underlies the PTAS construction (Lemma 2.1, Section 2.1)."
  },
  "domain": "claim-bound-structural",
  "orid": "vqxprtjuKH",
  "space_id": "neonforestmist/allocating-variance-maximize-expectation-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:00:26.024333+00:00"
}