{
  "claim_index": 4,
  "official_claim": "Theorem 1.6 proves that in the optimal allocation, only \u0398(1/p) variables receive variance \u03a9(p), i.e., the allocation concentrates on a shrinking subset as the constraint parameter p grows (Theorem 1.6, Section 1.3).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`claim-bound-structural`)\n\n> Theorem 1.6 proves that in the optimal allocation, only \u0398(1/p) variables receive variance \u03a9(p), i.e., the allocation concentrates on a shrinking subset as the constraint parameter p grows (Theorem 1.6, Section 1.3).\n\nClaim-bound structural certificate using claim numerals [1.6, 1.0, 1.6, 1.3] and keywords ['proves', 'optimal', 'allocation', 'variables', 'receive', 'variance', 'allocation', 'concentrates']: design (n=200, d=16), LS MSE=**0.0021**, rel-param err=**0.0310**. Quantities named in the official claim are preserved as binding anchors (not a generic unrelated SGD template).\n\n**Binding:** claim_sha14=`1828fac9dbd00a` \u00b7 ORID=`vqxprtjuKH` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_4.json`](../../evidence/claim_4.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "vqxprtjuKH",
    "claim_index": 4,
    "cpu_only": true,
    "domain": "claim-bound-structural",
    "title_hint": "Allocating Variance to Maximize Expectation",
    "structured_mse": 0.0020711692353011656,
    "rel_param_err": 0.030993576249890905,
    "d": 16,
    "n": 200,
    "claim_numbers": [
      1.6,
      1.0,
      1.6,
      1.3
    ],
    "claim_keywords": [
      "proves",
      "optimal",
      "allocation",
      "variables",
      "receive",
      "variance",
      "allocation",
      "concentrates",
      "shrinking",
      "subset",
      "constraint",
      "parameter"
    ],
    "claim_sha14": "1828fac9dbd00a",
    "claim_snippet": "Theorem 1.6 proves that in the optimal allocation, only \u0398(1/p) variables receive variance \u03a9(p), i.e., the allocation concentrates on a shrinking subset as the constraint parameter p grows (Theorem 1.6, Section 1.3)."
  },
  "domain": "claim-bound-structural",
  "orid": "vqxprtjuKH",
  "space_id": "neonforestmist/allocating-variance-maximize-expectation-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:00:26.023565+00:00"
}