Persistent Uncertainty as a No-Absorbing-State Condition: Non-Encodability, Boundary Openness, and Metastable Classical Persistence

This work develops a constraint-level framework in which global uncertainty is irreducible and cannot be fully encoded within any finite, horizon-bounded domain. This non-encodability implies that all admissible physical systems are thermodynamically open at their boundaries, leading to persistent, irreducible perturbations. From this, a no-absorbing-state condition is derived: physically realizable systems cannot evolve into exact stationary or fully absorbing configurations. Instead, they exhibit metastable persistence maintained by a balance between coherence production, dissipation, and irreducible leakage. A minimal overlap-network toy model is introduced to illustrate these dynamics. The model shows that classical-looking stability can arise without exact stationarity, and that coherence thresholds allow small fluctuations to control phase behavior. The result is not a microscopic derivation but a constraint-level statement: exact equilibrium is inadmissible in the presence of observers, while classical structure emerges as a maintained, non-final state.