Curvature Regulation Without an Imposed Curvature Sink: Numerical Tests of the Minimal Covariant Einstein–Scalar Model

This paper investigates whether curvature-dependent suppression of a nonlinear scalar kinetic sector can prevent gravitational curvature growth without introducing an explicit curvature-damping mechanism. A minimal covariant Einstein–scalar–regulator–reservoir model is formulated and tested numerically in a diagonal Bianchi-I spacetime. The regulator responds to electric-Weyl curvature through a finite-response auxiliary field, while the scalar and reservoir sectors exchange energy–momentum consistently. No phenomenological curvature sink, artificial diffusion, direct tidal damping, or post-step constraint projection is introduced. A prospective scan of 720 regulated configurations identifies no admissible bounded-curvature candidate within the tested parameter domain. Of these, 278 trajectories reach the prescribed strong-curvature threshold, while 442 terminate through reservoir admissibility loss. Matched-initial-state comparisons, independent numerical solvers, and tolerance-refinement tests support the reported classifications. High-curvature trajectories exhibit reproducible asymptotic scaling. The nonlinear scalar regulator becomes strongly activated, yet anisotropic Weyl-curvature growth persists. The central finding is that regulator activation does not, by itself, establish gravitational curvature regulation. Suppression of the nonlinear scalar constitutive response is insufficient to guarantee the sign-definite feedback required to arrest anisotropic collapse in the tested system. These findings constrain the minimal covariant curvature-regulation mechanism but do not constitute a general no-go theorem for curvature-regulated gravity. The work identifies the need for an additional, independently justified gravitational feedback mechanism.