Asymptotic consistency of the WSINDy algorithm in the limit of continuum data

The paper proves an exponential filtered concentration bound and unconditional asymptotic consistency for WSINDy under a moving-average filter with width m(ν) ≳ m^α, yielding t(m) = O(m^{-α(k/(d+1)-1/2)}) and tails exp{-c [m(t−t(m))]^{2/pmax}/(1+pmax)} (Theorem 4.2) , with a careful coupling argument to handle filter-induced correlations (Appendix D) and general concentration tools (Theorem 3.1) . The candidate solution reaches the same inequality and consequences (LS consistency and one-shot MSTLS support inclusion; exact recovery under an identifiability margin) and matches the rate/exponent and unions over KJ, but sketches independence or blocking for filtered averages rather than the paper’s coupling-based treatment of dependence. The conclusions and rates agree; the proof strategies differ.