Intelligence from First Principles: A Functional Model of Intelligence

We derive intelligence from first principles as a progression from systems to adaptive systems to functional models and, finally, to intelligence—characterized by generalization reach, orbit-based alignment, and contractive dynamics. We formalize updates as Markov kernels on a Polish conceptual space to obtain uniform Wasserstein contraction and orbit-based alignment, and augment contraction with a topology-aware folding operation that monotonically reduces topological complexity and increases spectral gap. This unifies distributional reliability guarantees with structural simplification. The resulting theory predicts—and we provide illustrative toy simulations—a finite-size criticality of cognitive compression (cognitive near-singularity) marked by variance peaks, bimodal latency distributions, and susceptibility scaling. We map the operators to dual-process cognition (regularized deterministic vs. stochastic kernels), working-memory load (Dobrushin-based slowdowns), schema acquisition (II→I conversion), and team composition (product-kernel closure), yielding falsifiable predictions and an estimation pipeline for contraction, topology, and criticality markers. The framework provides formal guarantees that are logically prior to empirical instantiation; full testing requires large-scale implementation of conceptual spaces engaging real error sinks. The framework further provides a generative basis for falsifiable models of how individual and collective intelligence evolve, with testable predictions about societal dynamics under different orders of intelligence implementation. Finally, we present a falsification protocol using 'error-sinks' and a dynamic minimality rule to keep the primitive function set small yet sufficient. At its core, the framework reduces to a simple discriminant: intelligence exists when coherence persists under recursive reformulation, with all other diagnostics serving as refinements of this invariance principle.