full-audit-v2/source_audit_v2.json

{
  "openreview_id": "vqxprtjuKH",
  "arxiv": "2502.18463",
  "claims": [
    {
      "claim": 1,
      "source_status": "confirmed",
      "source_page": 3,
      "anchor": "Section 1.2, Theorem 1.1",
      "note": "For VarAlloc with nonnegative means and fixed epsilon, the source gives a polynomial-in-n additive PTAS with E[max_i X_i] at least OPT-epsilon; independence is part of the VarAlloc definition."
    },
    {
      "claim": 2,
      "source_status": "confirmed",
      "source_page": 3,
      "anchor": "Section 1.2, Theorem 1.2",
      "note": "The source gives the same additive-epsilon polynomial-time guarantee for CorrVarAlloc. The displayed theorem uses a zero-mean notation, while Appendix A.2 handles nonnegative means."
    },
    {
      "claim": 3,
      "source_status": "confirmed",
      "source_page": 4,
      "anchor": "Section 1.2, Theorem 1.3",
      "note": "The theorem guarantees a polynomial-time Omega(1/log n) multiplicative approximation for GraphVarAlloc; the multiple-set setting is supplied by the surrounding problem definition."
    },
    {
      "claim": 4,
      "source_status": "misstated",
      "source_page": 4,
      "anchor": "Section 1.3, Theorem 1.6; Appendix B.1",
      "note": "The Theta(1/p) count and Omega(p) variance are only proved for Erdos-Renyi random GraphVarAlloc instances, asymptotically as n,m grow, with high probability. Here p is graph edge density, not a generic constraint parameter; the registered wording overgeneralizes to every optimum."
    },
    {
      "claim": 5,
      "source_status": "confirmed",
      "source_page": 7,
      "anchor": "Section 2.1, Lemma 2.1 and PTAS overview",
      "note": "For zero-mean, possibly correlated Gaussians with each variance at most epsilon squared and total variance at most one, the positive-part maximum is O(epsilon sqrt(log(1/epsilon))). The overview then retains only variances at least epsilon squared, leaving O(1/epsilon squared) variables."
    },
    {
      "claim": 6,
      "source_status": "confirmed",
      "source_page": 5,
      "anchor": "Section 1.3, Figures 1-2",
      "note": "The figures use Monte Carlo Erdos-Renyi GraphVarAlloc simulations with n=8 and p in {1/8,...,8/8}, covering independent, positive-correlation, and negative-correlation cases. Correlated experiments use 2-by-2 block-diagonal covariance matrices."
    }
  ],
  "upgrade_v2": {
    "scope": "page-anchored source audit plus independent numerical consequences",
    "claim_4_policy": "registered overgeneralization explicitly falsified; corrected theorem tested"
  }
}