The Kinematic-Substantial Octaplex (KSO): A Geometric Unification of Fundamental Constants via 24-Cell Lattice Projection

This paper proposes a geometric unification of the Standard Model and Cosmological Constant by modeling the universe as a kinematic 4-dimensional lattice based on the 24-Cell Octaplex. We demonstrate that the seemingly arbitrary parameters of physics are direct consequences of projecting this self-dual 4D geometry into 3D space.

Specifically, we show that the Kepler Conjecture sphere-packing limit (approx. 74%) corresponds to the observed Active Energy density (Dark Energy + Baryonic Matter), while the interstitial void fraction (approx. 26%) corresponds to Dark Matter. Furthermore, we derive the mass hierarchy of fundamental particles as fractal scalings of the lattice fracture (24^N) and lattice strain (H0), predicting the Top Quark and Electron masses to within 1-2% of experimental values. This model reduces the free parameters of the universe to a single input: the lattice velocity c.