A Nonsingular Horizon from Finite Update Capacity: A Radial Toy Model

This work introduces a minimal radial toy model showing how a finite geometric update capacity can eliminate singularities during gravitational collapse. Instead of allowing curvature to diverge, the model imposes an upper limit on expressible gravitational acceleration, denoted as g_cap. Once this limit is reached, the interior becomes a saturated region with finite curvature, and any additional mass forces the boundary to expand outward rather than deepening curvature. By applying this constraint to a post-collapse point mass, an analytic saturation radius emerges: r_sat(M) = √(G·M / g_cap) This radius marks the location where the GR acceleration demand first exceeds the curvature-expression limit. The result is a smooth, nonsingular interior and a mass-dependent boundary that scales as M^(1/2). Exterior to this radius, gravitational behavior remains indistinguishable from GR. Numerical checks confirm that once the interior is saturated, discretized radial models collapse the saturation boundary to the smallest resolvable radius, matching the analytic law. This demonstrates that strong-field divergence is not required for gravitational collapse. The model serves as a compact illustration of how finite-rate emergent geometric frameworks can naturally produce nonsingular horizons while recovering classical behavior externally.