Recursive Coordination Information Theory: Decision Sufficiency, Consequence Sufficiency, and Recursive Closure

Decision information is not evaluation information

An information interface can preserve every relative action cost required by a current decision and still omit distinctions needed to evaluate the circumstances that action creates. This paper develops Recursive Coordination Information Theory (RCIT) around that separation, within a common Coordination Information Theory (CIT) framework for task-relative information contracts and source contraction.

Declared current queries induce a decision interface, while action-conditioned successor queries induce an evaluation interface. Decision information supports the latter requirement exactly when the evaluation interface is a function of the decision interface.

The gap, its measure, and its closure

For finite deterministic interfaces under a specified source law, the conditional entropy of the evaluation interface given the decision interface is the minimum conditional information in a supplement that permits evaluation. A same-task construction makes this gap positive despite complete current-regret sufficiency.

Classical controlled-Markov refinement supplies recursive completion, whose conditional entropy measures the information added beyond the starting contract. Exact examples distinguish current sufficiency, recursive closure and reward-preserving abstraction, and show that individually closed contracts can require further information when joined.

Potential-based reward shaping and finite rational inattention provide connections to invariant task descriptions and the Nash-welfare form of the fixed-slope information–regret problem. Separate recursive-learning investigations examine evaluation provenance, persistence and externally supplied training targets.

What the paper does and does not claim

The framework characterises what an interface must retain for current use, successor evaluation and recursive coordination. Learning and acquiring that information remain distinct implementation questions. The entropy statements are for finite deterministic interfaces under a specified source law, and the recursive completion construction assumes the finite controlled-kernel setting in which it is stated.

Place in Coordination Information Theory

This paper names Coordination Information Theory (CIT) as the common framework of task-relative information contracts and task-sufficient contraction, which came first and do not use the name, and extends it from current decisions to the circumstances those decisions create.