Mathematical formalism of Ze

This article introduces and formalizes Ze, a novel theoretical framework for cognitive architecture and autonomous systems. Ze posits that advanced intelligence requires the maintenance of two distinct, asymmetric generative models of the same environment: a causal (forward) model MA\mathcal{M}_AMA​ and a counterfactual (inverse) model MB\mathcal{M}_BMB​. Each model minimizes its own variational free energy FA\mathcal{F}_AFA​, FB\mathcal{F}_BFB​, and their interaction dynamics define core cognitive processes. A key emergent quantity is the model conflict ΔF=∣FA−FB∣\Delta \mathcal{F} = |\mathcal{F}_A - \mathcal{F}_B|ΔF=∣FA​−FB​∣, which regulates a phase transition between two fundamental regimes: an…