The Principle of Least Computational Action

This paper proposes that biological evolution operates under a composite optimization principle balancing physical action against informational verification cost. By introducing the control parameter ρ (ratio of Verification Load to Verification Capacity), we demonstrate that biological systems exhibit three distinct dynamical regimes: Flow (ρ < 1) characterized by continuous exploration, Snap/Termination (ρ ≈ 1) characterized by discrete transitions, and Crash (ρ > 1) characterized by constraint abandonment.We formalize evolution as minimizing S[x(t)] = ∫L dt + λK_Levin(x), where the Levin complexity term represents the computational cost of generating and verifying biological structure. Two biological instantiations demonstrate this framework: photosynthetic energy transport as a Flow regime example, and enzymatic catalysis as a Snap regime example.This framework recasts evolution as a subtractive process where complexity survives only insofar as it can be continuously verified within finite metabolic, temporal, and error-tolerance resources. The same formal structure appears to generalize beyond biology to physical, cognitive, and computational systems, suggesting substrate-independent optimization principles govern structured reality.