Cross-Platform Metrological Paradigm for Unified Phase--Frequency Readout: Windowed Upper Limits on FRB Vacuum Polarization, Spectral--Scattering Equivalence and Identifiability of \delta-Ring--AB Flux, and Critical Coupling Metrology for Scattering Topological Invariants

Propose unified metrological paradigm using "phase--frequency" as sole readout, penetrating three classes of systems with disparate scales and physical backgrounds: fast radio burst (FRB) propagation at cosmological distances, point interactions (\delta potential) and Aharonov--Bohm (AB) flux coupling in cold atom/electronics one-dimensional ring systems, and scattering topological invariants for condensed matter class D endpoints. Under unified kernel--windowing--generalized least squares/Fishe