The Principle of Least Computational Action: Physical Instantiation

This paper demonstrates that physical evolution operates under a composite optimization principle balancing physical action against informational verification cost. Using the control parameter ρ (ratio of Verification Load to Verification Capacity), we show that physical systems exhibit three dynamical regimes: Flow (ρ < 1) with continuous state-space exploration, Snap/Termination (ρ ≈ 1) with discrete transitions, and Crash (ρ > 1) with structural collapse.Physical systems minimize S[x(t)] = ∫L dt + λK_Levin(x), where Levin complexity quantifies the computational cost of verification. We demonstrate this framework through two instantiations: quantum measurement as a Snap regime where decoherence saturates verification capacity, and event horizons as verification boundaries where causal bandwidth limitations create informational boundaries.This framework recasts physical evolution as a subtractive process where structure survives only insofar as it can be continuously verified against causal constraints and conservation laws. The same formal structure appears to generalize beyond physics to biological, cognitive, and computational systems. The Residue Cooling Hypothesis (Q_cooling ∝ αC²) provides testable predictions for datacenter thermodynamics.