Extended Simulations and Applications of the Prime-Induced Function Switching Model (PIFSM)

This article presents a comprehensive extension of the Prime-Induced Function Switching Model (PIFSM), focusing on large-scale simulations and practical applications. Building on the foundational framework introduced in the first paper, we explore functional switching behavior up to n = 1000, analyzing patterns of prime-induced discontinuities and non-monotonic transformations. The work includes:

Complete mathematical formulation of dynamic functional switching,

Tables and plots for numerical outputs of ,

Statistical analysis of average behavior, phase transitions, and variance over larger n,

Potential applications in cryptography, adaptive AI systems, bio-computational evolution, and decision logic.

This study deepens our understanding of discrete system evolution governed by prime structures and sets the stage for deploying PIFSM in practical computational contexts.