Numerical Extraction of a Coercive Vacuum Operator from Stationary Turbulent Dynamics.

We present a data-driven reconstruction of an effective linear operator governing a reconstructed scalar vacuum-tension proxy field $T_v(x,t)$ emerging from stationary turbulent dynamics within the TUO–NS framework. Without invoking any physical constants, SI calibration, or a priori field equations, we infer the dominant local second-order closure within a prescribed hypothesis class of PDE operators. Using large-scale numerical simulations, robust stationarity diagnostics, and high-statistics ordinary least squares regression over more than $10^6$ spacetime points, we show that the dynamics is accurately described by a damped wave operator: $$\partial_{tt} T_v = v_0^2 \nabla^2 T_v - \gamma \partial_t T_v - \omega_0^2 T_v$$ We obtain strong explanatory power both in-sample ($R^2_{\text{fit}} \approx 0.931$) and under a strict time-block hold-out validation ($R^2_{\text{held-out}} \approx 0.957$). Coefficients remain stable under block-bootstrap resampling and stationarity-threshold variations. The extracted operator admits a coercive quadratic energy functional with a bounded stationary sector in the selected regime. Reproducibility is ensured by an immutable archived bundle containing the reference script, run report, machine-readable diagnostics, and generated figures. The run report RUN_REPORT.json records the train/held-out frame indices, both $R^2$ scores, and traceability identifiers (script_name, bundle_name) linking this manuscript to the archived bundle. Auxiliary dispersion diagnostics may be marked inconclusive when insufficient oscillatory low-wavenumber modes are detected, without affecting the primary PDE regression result.