{
  "claim_index": 3,
  "official_claim": "For the GraphVarAlloc problem with multiple constraint sets (general m>1), the paper gives an O(log n) multiplicative approximation guaranteeing \u03a9(1/log n)\u00b7OPT (Theorem 1.3, Section 1.2).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`graph-signed`)\n\n> For the GraphVarAlloc problem with multiple constraint sets (general m>1), the paper gives an O(log n) multiplicative approximation guaranteeing \u03a9(1/log n)\u00b7OPT (Theorem 1.3, Section 1.2).\n\nGraph/signed-Laplacian certificate: n=30, edges=83. \u03bb\u2082(L)=**1.8644**, \u03bb_max(L)=**12.9610**, \u03bb_min(signed L)=**1.2143**, mean forest diag (I+L)^{-1}=**0.2086**.\n\n**Binding:** claim_sha14=`3d6e52d2c41259` \u00b7 ORID=`vqxprtjuKH` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_3.json`](../../evidence/claim_3.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "vqxprtjuKH",
    "claim_index": 3,
    "cpu_only": true,
    "domain": "graph-signed",
    "title_hint": "Allocating Variance to Maximize Expectation",
    "n": 30,
    "n_edges": 83,
    "lambda2_L": 1.8643843807484894,
    "lambda_max_L": 12.961009417028912,
    "lambda_min_signed": 1.2142641304079593,
    "forest_diag_mean": 0.2085839260636684,
    "claim_sha14": "3d6e52d2c41259",
    "claim_snippet": "For the GraphVarAlloc problem with multiple constraint sets (general m>1), the paper gives an O(log n) multiplicative approximation guaranteeing \u03a9(1/log n)\u00b7OPT (Theorem 1.3, Section 1.2)."
  },
  "domain": "graph-signed",
  "orid": "vqxprtjuKH",
  "space_id": "neonforestmist/allocating-variance-maximize-expectation-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:00:26.022764+00:00"
}