Benchmark-Relative Temporal-Resolution Sufficiency for Wearable Time-Series Learning

A wearable system must choose temporal resolution before a downstream representation can exploit the signal. Conventional resolution sweeps rank tested configurations, but they do not define when a cheaper rate–representation pair preserves enough utility to remain acceptable. We formulate this as *benchmark-relative temporal-resolution sufficiency*. A declared tolerance first defines an admissible set relative to the best tested reference; deployment costs are considered only inside that set. This yields a single decision chain from *admissibility* to *preference* to *validity*. We characterize how the admissible set changes with tolerance, reference strength, target environments, and budgets; give an exact finite-grid extraction algorithm; separate oracle information loss from fitted-model reversals; and derive a uniform-error condition under which the empirical sufficient set and frontier are stable. Across UCI HAR, HAR70+, and Daphnet, a one-point macro-F1 tolerance changes the minimum tested rate from best-score references at 10, 10, and 64 Hz to sufficient rates at 5, 10, and 32 Hz. Class-specific, cross-cohort, perturbation, data-volume, and cost analyses then identify when those decisions cease to be adequate. The contribution is therefore not a universal sampling threshold, but a formal account of when a finite resolution comparison supports a lower-cost design decision and what evidence is required for that decision to remain valid.