Galactic Disks as Radial Resonance Structures: Operational Definition, Minimal Dynamics, and Merger Falsification Tests

This document introduces a quantitatively testable interpretation of galactic disks and halos as weak radial resonance-gradient structures. An operational mismatch proxy, Δf (r) = Ωₒrb (r) − κ (r) /2, is defined directly from observable rotation curves and epicyclic frequency profiles. This proxy can be computed from observational data, mass models, or simulation outputs. A minimal radial dynamical model is developed showing that local minima in Δf (r) can bias orbital density and produce weak shell or ring layering. During merger events, time-dependent gravitational potentials amplify this structuring. The manuscript provides: • An operational and computable definition of the resonance mismatch • A minimal dynamical trapping model • A quantitative shell amplitude normalization • A merger-age exponential decay prediction • Order-of-magnitude scaling examples • Observability thresholds for density and kinematic modulation • A full falsifiable observational and simulation pipeline A key quantitative prediction is: Aₛhell (t) = A0 exp (−t / τᵣelax), with τᵣelax ≈ 1 / κ (r). This allows direct testing using merger-age binned galaxy samples. The full radial profile Δf (r) is interpreted as a galaxy’s dynamical resonance fingerprint, reflecting its formation and merger history. The hypothesis is falsifiable if shell regularity, kinematic modulation, and age evolution are fully reproduced by standard collisionless N-body models without additional resonance-layer amplification. Merger systems serve as the decisive laboratory for testing the model. This document is conceptual and test-oriented, not a data release.