Characterizing Open-Ended Evolution Through Undecidability Mechanisms in Random Boolean Networks

arXiv:2512.15534v2 Announce Type: replace
Abstract: Discrete dynamical models underpin systems biology, but we still lack substrate-agnostic diagnostics for when such models can sustain genuinely open-ended evolution (OEE): the continual production of novel phenotypes rather than eventual settling. We introduce a simple, model-independent metric, Omega, that quantifies OEE as the residence-time-weighted average of attractor cycle lengths across the sequence of attractors realized over time. Omega is zero for single-attractor dynamics and grows with the number and persistence of distinct cyclic phenotypes, separating enduring innovation from transient noise. Using Random Boolean Networks (RBNs) as a unifying testbed, we compare classical Boolean dynamics with biologically motivated non-classical mechanisms (probabilistic context switching, annealed rule mutation, paraconsistent logic, modal necessary/possible gating, and quantum-inspired superposition/paired-state coupling) under homogeneous and heterogeneous updating schemes. Our results support the view that undecidability-adjacent, state-dependent mechanisms — implemented as probabilistic context switching, modal necessity/possibility gating, paraconsistent logic (controlled contradictions), or quantum-inspired superposition/paired-state coupling (correlated branching) — are enabling conditions for sustained novelty. At the end of our manuscript we outline a practical extension of Omega to continuous/hybrid state spaces, positioning Omega as a portable benchmark for OEE in discrete biological modeling and a guide for engineering evolvable synthetic circuits.