Constraint Accumulation via Laziness in Finite Markov Chains - A Provable Specialization of the FIT Framework

The F-I-T (Force–Information–Time) framework aims to characterize evolutionary and learning dynamics through constraint accumulation and temporal structure. However, to move from an interpretive framework toward a mathematically defensible theory, FIT requires at least one rigorously analyzable specialization. In this work, we present a first provable specialization of FIT within the sandbox of finite-state Markov chains. By introducing a controlled hardening path via lazy transitions, we show that system constraints-defined as predictive mutual information-tend to their maximal value, while information production-measured by entropy rate-tends to zero. Under a simple self-dominance condition, these trends are monotone along the hardening path. This process admits a precise limiting interpretation of FIT's proposed "nirvana" state. Our results demonstrate that FIT-style claims can be transformed into concrete, falsifiable mathematical statements within an established probabilistic framework.