Minimal Irreversible Units: Operational Irreversibility and the Emergence of Historical Constraint in Digital Systems

We propose the concept of a Minimal Irreversible Unit (MIU): a formally definable,operationally detectable phase transition in digital or symbolic systems wherehistorical reconstruction becomes impossible under admissible interventions.Unlike notions of artificial consciousness or agency, MIU makes no claims aboutsubjectivity or intelligence.Instead, it characterizes the minimal condition under which a digital systemacquires an irreducible historical dependency.We provide an operational definition of irreversibility, introduce prime-indexednon-periodic perturbations as a sufficient obstruction to inversion,and define third-party detectable criteria for MIU emergence.We further demonstrate why periodic, chaotic, and algorithmically compressibleprocesses fail to induce MIU-level irreversibility.