We propose a finite-window temporal diagnostic for selected near-integrable Hamiltonian systems. It compares a normalized Fourier statistic of the perturbation Hessian along trajectories with a separately normalized finite-time redistribution estimator. We derive the log-frequency quotient derivative and state the positivity, calibration, coordinate, trajectory, and window dependencies that limit its interpretation. A deterministic 36-trajectory exploratory run compares four proxy statistics against an exploratory spectator-advantage label. After correcting the canonical modal projection and fixing the physical window, the best proxy has AUC 0.51029 (bootstrap 95% interval 0.30864--0.71193; one-sided permutation p=0.474). It exceeds the input-coordinate baseline by 0.05350, but a paired score-swap test gives p=0.401. The experiment therefore supplies no evidence of predictive value beyond that baseline. The proposed threshold must be fit and tested out of sample against an independent invariant-torus or chaos diagnostic. Maturity: Short Draft. Part of The Latent research program. Related papers in this program: Universal.