From Geometry to Logic: A Causal Ontology for Physical Law

This paper explores the nature of geometry in the Computed Universe (CU) model — a physics framework where reality emerges from causal updates propagating across discrete voxelated surfaces. Unlike traditional formulations in general relativity which rely on smooth differentiable manifolds, the CU model interprets geometric structure as the result of causal effort over expanding surface shells.<br>Key contributions include:<br>A reformulation of geometry as <b>surface-normalized causal saturation</b> rather than curvature in a metric space.An explanation of <b>gravitational weakening</b> due to fanout dilution over spherical shell geometries.Derivation of curvature as an emergent outcome of <b>update density per unit surface</b>.A coherent account of <b>shell-based gravitational propagation</b>, where mass-energy influences geometry through saturation limits, not warping.<br><br>This geometric foundation enables a unified explanation of spacetime curvature, gravitational behavior, and energy conservation from a substrate-level model. It also sets the stage for deriving Einstein’s field equations, Planck-scale thresholds, and quantum geometrical phenomena as emergent from shell-based causal structure.<br>The paper complements others in the CU series and offers a mechanistic reinterpretation of geometry, suitable for integration into quantum gravity, cosmology, and computational physics frameworks.