Bounded Agency: An Entropy-Constrained Calculusfor Sparse Semantic Agents

This paper propose a formal framework for AIagents that unifies semantic reasoning with resource-aware con-trol. Agents act via sparse policies over structured semantic fields,bounded by entropy and sparsity budgets. We define a typedoperational semantics, prove soundness and stability, and derivea sparse free-energy objective with phase transitions. The calculusis categorically structured, maps to unistochastic dynamics, andcompiles to executable policies with verified runtime bounds.This yields a foundation for interpretable, thermodynamically-plausible agent design.