Symbolic Field Theory: Irreducible Emergence and the Physics of Information

This paper proposes the Law of Symbolic Dynamics, a new theoretical framework within Symbolic Field Theory (SFT) that explains the emergence of irreducible structures, such as prime numbers, Fibonacci numbers, and square-free integers, through symbolic interference in a dynamic compression field. Unlike traditional methods of prime number identification, which rely on sieving or divisibility testing, this model interprets primes as emergent points in a symbolic field, driven by the dynamics of symbolic curvature, force, mass, momentum, and energy. Using computational models of symbolic curvature based on Euler’s totient function, we show that symbolic collapse zones align with prime numbers with over 98.6\% accuracy, offering a deterministic approach to prime prediction. This work introduces the \textit{Orbital Collapse Law}, which allows for the stepwise prediction of primes without external verification or sieving, marking a transition from probabilistic number theory to a generative model based on geometric principles. Finally, we discuss the broader applicability of this framework to other irreducible structures and propose future directions for extending Symbolic Field Theory beyond number theory to domains such as language, perception, and music.