Harmonic Vector Equilibrium: A Unified Integer-Based Framework for Control, Navigation, and Communication on the Cuboctahedral Matrix

This disclosure presents an integer-based spatial and phase control framework designed for embedded systems and actuators. The method replaces conventional floating-point arithmetic and 360-degree or radian metrics with a base resolution of L = 27720. This specific metric, being the Least Common Multiple (LCM) of integers 1 through 12, guarantees exact integer division for complex mechanical gear ratios and spatial subdivisions. The framework eliminates progressive floating-point phase drift and provides a computationally lightweight, pure-integer control law suitable for resource-constrained microcontrollers. The mathematical principle is inherently scalable to higher-precision systems for cross-disciplinary applications, including Magnetic Resonance Imaging (MRI), non-invasive neuromodulation (temporal interference), plasma confinement, and telecommunications. The complete C implementation and LUT generators are available as open-source prior art at the associated GitHub repository.