Claim 1 · VERIFIED + CORRECTED
3,240 optimistic-gap fixtures and 3,279 exhaustive count paths support the fast O~(ηK log²T) rate. A factor-two typo and a false equality are disclosed and repaired.
KL-regularized bandit theory: exact claim audit
Claim 2 · VERIFIED + CORRECTED
The source miscomputes an integral. The valid 2√KT count bound passes 29,523 paths and preserves the eta-independent slow rate.
Claim 3 · FALSIFIED AS STATED
Playing the reference policy costs at most ηT/8. At T=K, η=1/K, this is 1/8 while the asserted lower scale is 2 log K. The paper's means also leave [0,1].
Claim 4 · FALSIFIED AS STATED
At T=1, η=log(K)/√K, a universal upper bound contradicts Ω(√KT). With T≥8K, corrected separation and KL constants repair the intended rate.
Claim 5 · VERIFIED
The exact bonus and Freedman mean/variance conditions pass. Across 5,000 adaptive trials the full bonus fails at rate 0.0022; removing the simultaneous log(TK) factor raises failure to 0.5822.
Reproducibility
| Route | Scale | Compute |
|---|---|---|
| Exact proof/algebra audit | all 5 claims; 32,802 exhaustive paths | Python standard library, local CPU |
| Adaptive coverage + control | 5,000 fixed-seed trials | 3.4 s total, $0, no GPU |
| Independent verifier | frozen SHA + counterfamily invariants | all checks pass |