arXiv:2601.00632v1 · OpenReview IQojX8HugF
| Claim | Verdict | Headline |
|---|---|---|
| 1 LBW closed-form barycenter | reproduced | exact to 1e−14; BW needs ~12 iters, LBW 0 (87× faster) |
| 2 CBO particle system | reproduced | matches a literal per-particle implementation exactly |
| 3 Theorem 4.1 → global minimizers | falsified | gives a near-optimal energy bound; σ=5 breaks C₁>0 |
| 4 Lemma 4.1 under local Lipschitz | falsified | assumes growth-weighted Lipschitz; ratio unbounded |
| 5 CBO beats BWGF on A–D | falsified | CBO loses on B (+0.107) and D (+0.060) |
| 6 Extended exp map preserves PSD | reproduced | 20k draws, 68% outside the cone, all PSD |