Regular Simplex Hierarchical Gravity (RSHG): A Discrete Computational Framework for the Derivation of Physical Constants

One of the most profound challenges in modern physics lies in reconciling higher-dimensional theoretical frameworks with the observed 3+1-dimensional spacetime. This paper proposes Regular Simplex Hierarchical Gravity (RSHG), a theory that redefines spacetime as a consequence of dimensional reduction from a 4D bulk crystal to a 3D brane, where geometric frustration drives the emergence of physical constants and dynamics. At the core of RSHG is a fundamental duality: geometric perfection in 4D versus geometric frustration in 3D. We model the 4D bulk as a 600-cell crystalline lattice tiling the 3-sphere (S3),composed of regular tetrahedral 3-cells that achieve seamless tessellation—a continuous, frictionless structure with zero deficit angle. However, when this configuration undergoes dimensional reduction to a 3D brane, the intrinsic non-tessellability of these regular tetrahedra in flat Euclidean space introduces a persistent deficit angle of δ ≈ 7.36◦at each edge. This geometric obstruction triggers a phase transition from continuous symmetry to a discrete computational lattice. We demonstrate mathematically that gravity, inertial mass, and the arrow of time are not fundamental inputs but emergent computational residues—the irreducible processing load required to maintain consistency in a geometrically frustrated lattice. By deriving the gravitational constant G to within 1.1% of CODATA values and providing a geometric resolution to the cosmological constant problem, RSHG offers a rigorous, falsifiable bridge between discrete geometry and relativistic physics. (Collaboration with generative AI)