Neumann Project (VN-05): Evolutionary Core of Discrete Sine-Gordon Resonance and Fourier Modal Transit Within the Zohar Matrix

This dataset and software component represent the third research iteration within the Neumann Project (VonNeumann-0.5 / VN-05) meta-framework. Moving beyond static spatial compactification models, this work establishes the "Evolutionary Core" designed to simulate non-linear discrete lattice vibrations inside a closed 20-vertex Zohar matrix topological singularity (Register 0x0C). The computational core models a discretized Sine-Gordon Lagrangian over a periodic mesh, utilizing a 2nd-order symplectic Velocity Verlet integration scheme to ensure long-term Hamiltonian conservation. Real Fast Fourier Transformation (RFFT) spatial analysis is integrated directly into the runtime environment to track and verify the deterministic phase transit of energy across stable non-linear vibrational modes. This repository includes:1. The mathematical and physical formalization of the discrete Sine-Gordon resonance within the Zohar matrix framework.2. The vectorized, production-ready Python simulation engine leveraging NumPy for exact numerical integration and spatial modal profiling.3. The complete LaTeX source code for academic replication and verification. References and Project Heritage:- Phase 1: DOI 10.5281/zenodo.21269257 (Project: VonNeumann-0.5 Basis)- Phase 2: DOI 10.5281/zenodo.21282460 (Structural Matrices)