Coherent Long-Wavelength Modes in Galaxy Rotation Curves: Evidence from Unified Modelling, FFT, and Wavelet Analysis

We analyse high-quality galaxy rotation curves using a flexible unified gravitationalmodel and examine the residuals with Fourier and wavelet techniques.After subtracting the unified model, the residuals reveal smooth, long-wavelengthoscillations with characteristic scales of 5–15 kpc, extending beyond 50 kpc inextreme cases. These modes are radially persistent, robust to bootstrap resampling,and consistent between FFT peak frequencies and wavelet ridge extraction.We define a coherence strength score combining volatility, unified-modelpreference, and residual amplitude, and identify a top-five subset of galaxieswith the clearest signatures. The scale, persistence, and cross-diagnosticagreement of the coherence mode are difficult to reconcile with collisionlessdark-matter dynamics or local baryonic structure, suggesting instead a global,wave-like dynamical feature of the gravitational field or dark sector.