Echoes LIGO VIRGA

We investigate the possible presence of gravitational-wave echoes arising from a discrete scale-invariant structure in the post-merger phase of compact object coalescences. Instead of modeling echoes through specific boundary conditions, cavities, or exotic compact object assumptions, we adopt a parameter-free approach based on the existence of a closed variational coherence structure. We show that, if the post-merger dynamics admits a self-consistent coherent regime, the temporal separation, characteristic frequencies, and amplitudes of successive echoes must obey universal discrete scaling relations. In particular, the ratios between consecutive echo delays, frequencies, and amplitudes are predicted to converge toward fixed dimensionless constants, independent of the total mass, spin, equation of state, or microscopic horizon structure. This framework does not introduce any fundamental length scale, resonance frequency, or periodic cavity, but instead predicts a finite hierarchy of echoes governed by discrete scale invariance, with a natural upper bound on the number of observable coherent modes. The resulting predictions are directly testable with current and next-generation gravitational-wave detectors using model-independent, dimensionless observables. The analysis provides a falsifiable alternative to conventional echo models and establishes a clear observational criterion to discriminate between purely transient post-merger noise and genuine coherent echo structures.