Persistence Theory and the Taoian Universe: Iterative Structure, Functional Redundancy, and the Entropic Decay of Reversibility

In this paper, we explore a unifying conceptual bridge between Persistence Theory and Terence Tao’s vision of the mathematical universe. We propose that our physical universe may be modeled as a thermodynamically constrained substructure within a broader mathematical space — one characterized by iterative structure formation, finite redundancy, and entropy-driven degradation of reversibility. We formalize this perspective by proposing dynamic decay laws for the reversibility parameter eta, and explore how this degradation reflects a swing-back mechanism that becomes less effective across entropy-weighted iterations. This view reframes time, cosmological aging, and the arrow of entropy as emergent consequences of decreasing persistence across a mathematically embedded process.