Dynamic Substrate Theory (DST) — Observational Constraints and Adversarial Stress-Test Against LVK (LIGO-Virgo-KAGRA) Data

Abstract Replacing empty geometric spacetime with a physical continuous medium—the Maxwell-Oldroyd-B viscoelastic vacuum proposed by the Dynamic Substrate Theory (DST)—resolves profound conceptual gaps regarding inertia, dark energy, and fundamental fields. However, any theoretical framework modifying gravity must withstand high-precision observational constraints from international gravitational-wave consortia. In this work, we perform an adversarial stress-test on DST, evaluating gravitational wave propagation through a substrate endowed with elasticity and stress memory. By analyzing frequency-dependent phase velocity dispersion relations and expanding in the operational frequency regime of LIGO/Virgo (\sim 100\text{ Hz}), we derive strict analytical bounds for the difference between the substrate's relaxation and retardation times (\Delta\lambda \le 5 \times 10^{-20}\text{ s}). This confirms that the DST vacuum exhibits nearly instantaneous local elastic behavior, ensuring complete compatibility with the multi-messenger constraints of GW170817 and safeguarding the framework against empirical falsification. Keywords: Observational Constraints, Gravitational Waves, LVK Data, Maxwell-Oldroyd-B Vacuum, Viscoelastic Dispersion, Adversarial Stress-Test.