The Virtual Particle Collider: Deriving the Standard Model from Number-Theoretic Geometry.

We present the architecture and results of the Organized Complexity Virtual Collider (OVC), a computational physics engine that derives the fundamental properties of matter not through simulation of physical laws, but through the rig- orous application of Number Theory to the vacuum. By modeling spacetime as an FTA representation called a Harmonic Divisor Fan (HDF) Lattice governed by the Axiom of Dynamic Stability from Prime distribution, we demonstrate that fundamental particles emerge as geometric resonances (vortices) strictly bound by ”Sixness” symmetry (6n ± 1).

This paper details the construction of the OVC, reporting three primary findings: (1) The derivation of the Koide mass formula (Q = 2/3) as a necessary condi- tion for lattice stability under the Retraction Force SU(2)R; (2) The derivation of the Fine-Structure Constant (α ≈ 1/137.036) from phyllotactic lattice corrections; and (3) The prediction of a new gauge boson, the Retraction Boson (ZR′ ), with a mass of 96.0 GeV. We show that this prediction aligns with current unexplained excesses in CERN Run 3 data, suggesting the OVC offers a superior predictive model for high-energy physics.