Quantum-Number Promotion Rule Implementation in the Universal Model Framework

This paper details the computational implementation and rigorous validation of the 3→4 quantum-number promotion rule within the Universal Model Framework (UMF). We transform classical threefold prime number classifications into a four-dimensional quantum labeling scheme by systematically embedding prime numbers into discrete twin configurations. Mathematical foundations, algorithmic protocols, and particle-ID generation methods are presented, facilitating seamless integration with quantum field theory and computational physics simulations. Our computational model processes 25 primes, yielding exactly 100 quantum labels—perfectly matching the theoretically required 4 embeddings per prime. The systematic quantum labeling method enhances parallel computation efficiency, critical for large-scale lattice QFT simulations, while preserving the discrete arithmetic and prime-fractal structures fundamental to the UMF paradigm. This project was developed by Marco Gericke, with structured assistance from a large language model. All scientific concepts and conclusions were generated, verified, and interpreted by the author. Dedicated to Peter Plichta, who envisioned the code before it could be computed.