The Predict–Verify–Act Trilemma in Complex Adaptive Systems

Abstract

We formalize a trilemma in online pipelines (instances of complex adaptive systems): within a single decision epoch, Predict (P), Verify (V), and Act (A) cannot be jointly max within a single decision epoch, Predict (P), Verify (V), and Act (A) cannot be jointly maximized. We identify one hard mechanism and one diagnostic dimension. (1) Latency: a verification lag τ competing with the action deadline Δ induces quantitative lower bounds λ(τ, Δ); in particular, when τ  Δ a zero gap is impossible (Theorem 1). (2) Noncommutativity: modeling Vτ , Aphys/Adisc, and E as operators, drift and reflexivity yield nonzero commutators and holonomy, making orderings intrinsically asymmetrical and motivating routing rather than a fixed sequence. We treat E as latent; the V –A result depends only on (τ, Δ). The framework clarifies design levers for routed AI systems and policy evaluation.

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