Irreversible Emergence from Self-Referential Closure

We investigate the minimal conditions under which any concept becomes definable in a completely structureless system. Starting from an undifferentiated totality with no predefined notions such as space, time, or probability, we show that self-reference is the only admissible structure. We demonstrate that global constraints on recursive deviation necessarily lead to a zeta-like structure, whose convergence defines the emergence of irreversibility and the possibility of physical concepts.