Equation-Free Screening of Mittag–Leffler Compatibility from Multi-Horizon Relaxation Profiles

We study an equation-free screen for finite-window Mittag–Leffler compatibility, in which multi-horizon relaxation profiles are constructed out of sample by k-nearest-neighbor prediction from ensembles of scalar trajectories and compared with candidate temporal laws. The screen assesses compatibility, not the generating mechanism. In a matched, noise-free calibration, it reproduces the generating Mittag–Leffler behavior to numerical precision, while relaxation-rate heterogeneity shifts the fitted Mittag–Leffler order toward lower values. For noise-free classical distributed-rate ensembles, a Mittag–Leffler preference over a single exponential disappears when a biexponential alternative is included. Under observational noise, this recovery is incomplete: with three candidate families, the Mittag–Leffler law is still selected in 60% of runs for a classical ensemble, against 72% for a fractional reference. In the tested noise-free settings, simpler profile constructions reproduce the screening decisions, whereas kNN predicts individual trajectories far more accurately than a constant predictor. The screening interpretation of a single-record example, initially investigated as a chaotic test case, is withdrawn as evidence about the continuous system after numerical verification revealed a nonrobust simulated regime. Mittag–Leffler compatibility is therefore a comparative, condition-dependent screening outcome, not identification of fractional origin.