Intelligence as Cross-Scale Alignment: A Divergence-Minimization Framework for Decision and Observation

This work introduces a formal framework in which intelligence is defined as the rate of cross-scale divergence compression in a coupled system. Rather than treating intelligence as an intrinsic property of an isolated agent, the framework models it as a relational quantity emerging at the interface between micro- and macro-operational scales, defined relative to a chosen scale pair (s₁, s₂) and a stochastic translation kernel T. Three propositions are established in derivational sequence: (1) observational frames are encoded in coupling geometry as boundary conditions prior to any measurement event; (2) frame activation is gradient descent on accumulated informational divergence — no agency is required at the moment of activation; and (3) intelligence is quantified as (s₁, s₂, t) = -ddt where is the KL divergence between cross-scale state distributions. The framework is operationalized through the A → O → I → F → A loop, a closed dynamical system in which agent state, observation, interaction, and field mutually co-determine one another. The structural condition for sustained Ξ > 0 is loop closure: the field F must retain the informational trace of prior interactions. The framework is instantiated concretely in trajectory navigation, connecting to the Information-Entropic Navigation (IEN) paradigm. Intelligence, in this formalization, does not belong to a system. It emerges at the boundary when systems couple correctly across scales.