From Momentum Cubed to Curvature Quantized: A Generative Foundation for Physics from First Principles

This paper introduces two foundational causal-geometric equations that together form a generative basis for all known physical laws:<br>E = p^3/c: a general energy identity replacing E = mc^2, modeling energy as volumetric momentum propagation across causal fanout surfaces.RP.(tP.c)^2 = 6: a curvature constraint linking gravitational curvature to causal update density within a spherical voxel of radius lP.<br><br>These identities emerge from the <i>Computed Universe (CU) model</i> — a theoretical framework in which spacetime, mass, energy, and force result from discrete, voxel-based causal updates that propagate at speed c.<br>In this model:<br><b>Energy</b> arises from momentum cubed and distributed over a causal surface geometry.<b>Curvature</b> reflects the intensity of surface-normalized update effort, bounded by a universal constant (6).<b>All major physical constants</b> — lP, EP, mP, FP, G, hbar — are derived systematically from a small set of causal primitives rather than being independently postulated.<br><br>This work shows how classical expressions (e.g., E = mc^2, Einstein’s field equations) naturally emerge as limiting cases of these more general and mechanistic identities. The model resolves long-standing fine-tuning problems, unifies gravity and quantum action, and reframes fundamental physics as an emergent phenomenon of surface-propagated causal computation.<br>The paper concludes with a roadmap for simulation, empirical validation, and further development within the CU framework. It forms part of a broader research series proposing the Computed Universe as a <i>General Theory of Reality</i>.