Cubic Phase Dispersion of Gravitational Waves from Finite Vacuum Response

This preprint derives a universal cubic phase–dispersion signature for gravitational waves propagating through a finite-response vacuum. Assuming a minimal causal transfer kernel characterized by a single Lorentz-invariant response time $\tau$, the accumulated propagation phase acquires a frequency-dependent correction with fixed exponent $\alpha=3$ and fixed negative sign. The resulting modification introduces zero additional free parameters beyond $\tau$ and source distance, making the prediction directly testable with public LIGO/Virgo/KAGRA data. The work provides a falsifiable phenomenological discriminator between finite vacuum response dynamics and standard massive-graviton or Lorentz-violating scenarios.