Predictive Bioharmonics: On the Structural Equivalence of Beginning and End in Definable Dynamical Systems

This manuscript explores a structural property that appears to arise in any system that is assumed to (i) be mathematically definable and (ii) exhibit dynamical evolution over more than a single step. Without invoking physical assumptions, empirical claims, or assertions of proof, the analysis examines whether such systems are implicitly constrained toward closure or recurrence. By considering definability, iteration, and domain consistency within a minimal mathematical framework, the paper argues that indefinitely non-returning evolution leads to a loss of definability and therefore undermines the system’s ability to exist as a coherent dynamical model. Under these assumptions, the distinction between “beginning” and “end” becomes structurally ambiguous and may collapse into a single mathematical element. No claim of proof or universal truth is made. The purpose is to present a logically consistent exploration that may serve as a conceptual lens across multiple domains.