Geometric Control of Quantum Time Delay in Non-Smooth Regimes: Operational Descriptors, Spectral Mechanism, Scaling Laws, and Falsifiability

This work introduces an operational geometric framework for analyzing Eisenbud–Wigner–Smith (EWS) time delay in non-smooth quantum regimes. Without modifying standard quantum mechanics, we define scale-dependent geometric proxies compatible with non-smooth metric-measure structures and connect them to spectral shift mechanisms via Krein theory. Two scaling regimes are distinguished and expressed through a falsifiable law τ(E;ℓ) ∝ (1 + X(ℓ))^γ. The framework explicitly preserves unitarity, no-signaling, and relativistic causality. Concrete falsifiability criteria (Types I–III) are formulated. Order-of-magnitude comparison with attosecond chronoscopy suggests compatibility with observed delay enhancements in reduced-dimensional systems. The work introduces no new fundamental fields; it reframes time-delay observables in terms of coarse-grained geometric descriptors.