Structural Theory of Everything

All enduring structures exist under a single unavoidable condition: not all distinc- tions can be preserved indefinitely. This work formalizes that condition as an axiomatic foundation for irreversible persistence. Beginning from the existence of at least one ir- reversibly excluded distinction, a minimal mathematical framework is constructed in which accessibility, absorption, order, probability, entropy, and limits of prediction arise 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 or domain-specific assumptions. Within this layer, irreversible loss is represented through absorbing subsets of an accessibility relation, and general constraints on persistence, learning, control, and representation are derived. Layer II provides interpretations of the same formal results across physical, biological, cognitive, institutional, and artificial systems, without introducing new mathematics. The framework does not explain why irreversibility exists, nor does it aim to replace existing scientific theories. It establishes instead what must be true of any system in which persistence under irreversible loss is possible at all. Here, “theory of everything” refers to universal structural necessity, not to explanatory or predictive completeness.