The missing timepiece: Optimal time allocation in the work-constraint cycle of autonomous agents

Kauffman's work-constraint (W-C) cycle captures the logical interdependence of work and constraint production in living systems, but leaves a fundamental dimension unexplored: when should each phase occur, and for how long? We argue that the relative duration of the work and constraint phases constitutes a temporal constraint that any autonomous agent must satisfy. Framing this as an optimal stopping problem, we show that the work phase should occupy 1/e ≈ 37% of the total cycle, which is the point at which diminishing returns on continued energy extraction are optimally balanced against the need for constraint reconstruction. We apply this framework to the eukaryotic cell cycle, treating G1 as the work phase and S/G2/M as the constraint phase, separated by the restriction point (R/START). Empirical observations from budding yeast and immortalized human cancer cells, which are systems that proliferate autonomously under steady-state conditions, show G1 durations of approximately 35-40% of the cell cycle, consistent with the 1/e prediction. Because cells lack explicit clocks, we propose that stochastic gene expression fluctuations may provide an implicit, representation-free mechanism for tracking elapsed time, and outline the empirical conditions needed to test this hypothesis. Our analysis suggests that temporal allocation deserves to be treated as a primary dimension of autonomous agency alongside the structural and thermodynamic dimensions already recognized.