Weyl-Electric Effective Closure in BSSN Numerical Relativity: Exploratory Strong-Field Regulation Tests

This work presents an exploratory numerical-relativity test framework motivated by an effective torsion/Weyl geometric response model. The main hypothesis investigated is whether spacetime, treated as an active geometric medium with storage-and-return behavior, can dynamically regulate strong-field General Relativity evolution through additional geometric response channels. Starting from an EFT-inspired Weyl-electric closure formulation, a modified BSSN evolution system is constructed in which an auxiliary geometric response tensor couples to the tracefree extrinsic curvature sector. The implementation is not a full action-derived torsion BSSN theory and should instead be interpreted as a phenomenological strong-field closure model designed to test nonlinear regulation mechanisms. The repository contains: the draft theoretical manuscript, Python/Numba numerical-relativity implementations, diagnostic and ablation tests, seed robustness tests, GR baseline comparisons, exploratory strong-field simulations. The numerical experiments indicate the appearance of nontrivial regulated regimes relative to pure GR baselines under specific EFT-inspired response couplings. In particular, regulation disappears under ablation tests when the Weyl-response coupling is removed, while regulated behavior persists across multiple random seeds under identical gauge conditions. Several important aspects remain incomplete and are left for future work, including: a fully covariant derivation of the nonlinear gating response, the EFT origin of the expansion-channel coupling, heavy-mode completion of the effective theory, hyperbolicity analysis, constraint propagation analysis, and full high-resolution NR validation studies. This upload should therefore be interpreted as a research-stage exploratory framework and numerical companion study rather than a finalized gravitational theory.