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.

ADDENDUM I: Discrete Geometric Stability in 4D Spacetime:  
Mathematical derivation of the Table of Croes and the correlation with the Eddington Number (24^58)

ADDENDUM II - THE GEOMETRIC ATLAS: A Visual Codex of the Quantum Universe

ADDENDUM III - Independent Verification of the 2010 KSO Framework & The Novel Geometric Derivation of the Electron

ADDENDA IV - VIII - Extension of the Geometric Atlas

ADDENDUM IX - The Geometric Origin of Inertia

ADDENDA X & XI - On the Hierarchy and the Cosmology