Cubic Phase Dispersion of Gravitational Waves from Finite Vacuum Response

This work 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 τ, we obtain a frequency-dependent phase correction with fixed exponent α = 3 and fixed negative sign. The predicted phase shift introduces zero additional free parameters beyond τ and source distance, making it directly testable using public LIGO/Virgo/KAGRA data. The result provides a clean phenomenological discriminator between finite vacuum response dynamics and existing massive-graviton or Lorentz-violating scenarios.