RaMu Virtual Probability Field: VPF Simulation Code v1_0

This document presents the complete source code (v1.0) and accompanying documentationfor the RaMu Virtual Probability Field (VPF) simulation. The code is a companion tothe paper “Emergent Probability from Deterministic Multiplicity: The RaMu Virtual ProbabilityField”. The simulation implements a 3D complex scalar field with a Mexican-hatpotential, demonstrating spontaneous U(1) symmetry breaking and topological defect (vortex)formation from purely deterministic classical field equations. No probabilistic elementsor random forces are introduced.Across multiple independent runs, the simulation consistently produces:• Early phase: high vortex multiplicity (∼600–700 defects)• Mid phase: rapid annihilation and coarsening• Late phase: convergence to 2–5 stable vortices (average 3.5)• Final probe densities: near-uniform (|ϕ|2 ≈ 1) with low variance• Kurtosis ∼8.35 indicating heavy-tailed condensationThese results provide computational evidence for the RaMu hypothesis: probabilityemerges from deterministic resolution of infinite multiplicity in a pre-probabilistic substrate(the Virtual Probability Field).