Unified Model of Causal Mathematics and Number Theory Structures

This paper introduces a unified framework that connects causal mathematics with number theory, proposing that the structure of causality in the universe mirrors the mathematical distinction between rational and irrational numbers. Drawing on the Causal Conservation Principle (CCP), Logical Causality Principle (LCP), and entropy dynamics, we argue that causal sequences behave analogously to rational (closed-loop) or irrational (non-terminating, non-repeating) processes. The model explores how persistent systems rely on recursive, computable, and closed causal structures, whereas divergent, entropy-amplifying phenomena correspond to causally “irrational” configurations that require external inputs to stabilize. By mapping entropy, causal decay, and information discontinuity onto number-theoretic analogies, this framework establishes a mathematical logic of persistence and collapse. Through this lens, entropy increase is not merely thermodynamic disorder but a consequence of causally divergent structures losing the ability to function as future inputs. The paper presents a formalization of these transitions and suggests potential applications in theoretical physics, information systems, and complexity theory. This work positions causal mathematics as a bridge between logical determinism and thermodynamic evolution.