The Lattice Continuum Model (LCM): A Geometric Framework for Fundamental Constants based on Truncated Octahedron Symmetry

The Lattice Continuum Model (LCM) proposes that the physical vacuum is a hyper-rigid solidstructured by Truncated Octahedron unit cells. We argue that while the Weaire-Phelan structureoffers a mathematical energy minimum for foams, the physical vacuum necessitates global isotropyto preserve conservation laws, favoring the truncated octahedron. We report a phenomenologicalcorrelation where the proton-to-electron mass ratio (mp/me) approximates 6π5 (≈ 1836.118) with99.99% precision, interpreted as a 5-dimensional phase-space topological volume constrained by thecell’s 6 orthogonal faces. Furthermore, we define the gravitational constant G as a derived propertyof the lattice’s 8π flux geometry, demonstrating its mathematical convergence to 4π isotropy atmacroscopic scales. A scale consistency check using solar lensing data validates the model with99.91% accuracy.