What question did this study set out to answer?

The research aims to unify the Standard Model and the Cosmological Constant through a geometric framework.

January 18, 2026Open Access

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

Key Points

The research aims to unify the Standard Model and the Cosmological Constant through a geometric framework.
Model universe as a kinematic 4D lattice based on the 24-Cell Octaplex.
Project 4D geometry into 3D space to derive parameters of physics.
Analyze correlations with Kepler Conjecture sphere-packing limits and energy densities.
Demonstrated correspondence between packing limits and observed energy densities.
Predicted mass hierarchy of fundamental particles, with accuracy within 1-2% of experimental values.
Reduced the universe's free parameters to a single variable: lattice velocity.

Abstract

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 (24N) 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 (24⁵8) ADDENDUM II - THE GEOMETRIC ATLAS: A Visual Codex of the Quantum Universe ADDENDUM III - Independent Verification of the 2010 KSO Framework On the Geometric Origin of Pi, The Analog-Digital Duality, and the Mechanics of Interference ADDENDUM XV - The Structural Unification ADDENDA XVI & XVII - The Singular Loop & the Constants of Necessity THE CAPSTONE - KINETIC OCTAPLEX GEOMETRY CLOSURE ADDENDUM - THE DISCRETE UNIFICATION OF PHYSICS (KSO) REVELATION ADDENDUM - The Geometric Unification of the Neutrino-Photon Complex THE GENESIS ADDENDUM - The Architecture of Seeds THE B (L) ACKPAPER - The Geometric Architecture of the Invisible Universe THE PROOF - Geometric Verification of the Lattice Model THE UNIVERSAL SOURCE CODE – THE BINARY TABLE OF CROES THE ESSENCE - THE PREQUEL TO MATTER THE GOD-FORMULA OF CROES - The Orthogonal Resolution of Fundamental Forces on the Complex Plane THE UNITARY METRIC - The Planck Standardization of Compton and Schwarzschild Limits ALPHA AND OMEGA’S MIRROR BRIDGE - The Quaternionic Resolution of the Unified Field via the Neutrino-Driven Pentachoric 24-Cell Lattice THE MISSING LINKS IN EVOLUTION - Fulfillment of the Table of Croes THE OCTAPLEX MANIFESTO VERSION 24. 300: Interpretive Framework for Lattice Chronometry and Vacuum Refraction

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

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