Universal Discrete Frequency Ratios in Post-Merger

We show that the post-merger phase of binary neutron star coalescences exhibits a discrete, scale-invariant frequency structure that does not depend on the microphysical equation of state, phenomenological fitting formulas, or dense-matter QCD modeling. Starting from a closed variational principle with no free parameters, we demonstrate that the remnant object behaves as a coherent macroscopic solution whose oscillation spectrum is governed by fixed universal ratios between characteristic frequencies. In particular, the dominant post-merger spectral peaks are shown to obey constant frequency ratios determined by the internal coherence of the variational solution, rather than by detailed compositional or thermodynamic assumptions. This leads to a discrete hierarchy of spectral lines instead of a continuous or model-dependent spectrum. The result provides a natural explanation for the recurrent frequency clustering observed in numerical simulations and gravitational-wave data analyses, without invoking ad hoc calibration to specific equations of state. We apply the framework to existing LIGO–Virgo events, showing that the observed post-merger frequency structures are already compatible with the predicted discrete ratios within current experimental uncertainties, despite having been previously interpreted using phenomenological models. The analysis yields a sharp, falsifiable prediction: any genuine post-merger signal must organize its spectral content according to the same universal ratios, independently of the progenitor masses and nuclear modeling. This work establishes post-merger gravitational-wave spectroscopy as a direct probe of an underlying closed generative principle, providing a new route to interpret compact-object dynamics beyond equation-of-state driven approaches.