Prime Number Emanation from the Existential Rhythm Field F(t): A New Mathematical and Physical Framework

Prime numbers have long been considered fundamental yet mysterious structures in mathematics. This study reinterprets prime numbers not as static numerical sequences but as emergent phenomena arising from the existential rhythm field F(t). By modeling F(t) as a superposition of rhythmic and fluctuating components, we demonstrate that prime emanations can be understood through rhythm interference and resonance mechanisms. Our approach provides a unified framework that connects number theory with nonlinear dynamics and offers new insights into the nonlinearity and local fluctuations of prime distributions. This work opens pathways for interdisciplinary applications across mathematics, physics, and complex systems.