2-Finite-size selection effects and Convergence Profiles in Deterministic Filtering of Normalized Mode Sums

We report numerical experiments on deterministic filtering procedures applied to linearly growing mode sums. Building on a general asymptotic framework based on subsequence density, we investigate finite-size effects and convergence profiles for several families of deterministic subsequences, including quasi-periodic constructions and sparse perturbations.
Our results provide a reproducible stress test against fine-tuning and document a hierarchy of convergence behaviors across different filtering rules.