Structural Theory of Everything I: An Axiomatic Theory of Irreversible Persistence

All enduring structures exist under a single unavoidable condition: not all distinctions can be preserved indefinitely. This work formalizes that condition as an axiomaticfoundation for irreversible persistence. Beginning from the existence of at least one irreversibly excluded distinction, a minimal mathematical framework is constructed inwhich accessibility, absorption, order, probability, entropy, and limits of predictionarise as necessary consequences rather than assumed primitives.The development proceeds in two strictly separated layers. Layer I is purely formal:only definitions, axioms, lemmas, and theorems are stated, without interpretation ordomain-specific assumptions. Within this layer, irreversible loss is represented throughabsorbing subsets of an accessibility relation, and general constraints on persistence,learning, control, and representation are derived. Layer II provides interpretations ofthe same formal results across physical, biological, cognitive, institutional, and artificialsystems, without introducing new mathematics.The framework does not explain why irreversibility exists, nor does it aim to replaceexisting scientific theories. It establishes instead what must be true of any system inwhich persistence under irreversible loss is possible at all. Here, “theory of everything”refers to universal structural necessity, not to explanatory or predictive completeness.