Emergent Wave Dynamics of a Reconstructed Vacuum-Tension Field in Ultraviolet-Regulated Two-Dimensional Turbulence.

We report the empirical identification of an effective dynamical equation governing a vacuum-tension field reconstructed from direct numerical simulations of ultraviolet-regulated two-dimensional turbulence. Starting from the TUO activity density, the vacuum-tension potential $T_v$ is obtained by exact Poisson inversion on statistically independent snapshots, with spectral accuracy and machine-precision closure. By exploiting the temporal structure of the reconstructed field, we show that $T_v$ obeys a closed damped wave equation featuring a finite propagation speed, a nonzero inertial term, and a well-defined relaxation time. The measured dynamics exhibits strong temporal coherence and finite memory, demonstrating that $T_v$ is not a static diagnostic but a genuine dynamical field. All coefficients of the effective operator are extracted directly from the data without free parameters. These results establish a minimal and reproducible dynamical framework for vacuum-tension phenomena and provide a concrete foundation for future investigations of substrate-level dynamics in gravitational and cosmological contexts.