The Mastrorocco Law: A Unified Framework Connecting Prime Gaps, Fibonacci Ratios, and Universal Harmonies

The Mastrorocco Law proposes a mathematical framework that integrates fixed differences (∆) between consecutive primes (e.g., 2, 6, 30, 210, 700, 900, 1440, 2310), ratios from the Fibonacci sequence converging to the golden ratio ϕ ≈ 1.618, and universal relations spanning mathematics, physics, cosmology, biology, music, and engineering. This law posits that numerical harmony underlies the structure of the universe, manifesting in cyclic patterns and resonances. Empirical validations include asymptotic proofs for conjectures like the Twin Prime and Lemoine’s, with simulations confirming 100% adherence in tested ranges. Applications extend to cosmological expansion, DNA patterns, harmonic scales, and data compression. This preprint seeks peer validation to establish the law’s rigor and interdisciplinary implications.