Algebraic Semantics of Governed Execution: Monoidal Categories, Effect Algebras, and Coterminous Boundaries

Alan L. McCann's new paper, 'Algebraic Semantics of Governed Execution,' presents a formal framework for ensuring AI systems operate within verified safety bounds. The work is fully mechanized in 32 Rocq modules comprising ~12,000 lines of code, with 454 theorems proved and zero admitted assumptions. At its core is a GovernanceAlgebra record with three axioms—safety, transparency, and properness—that induces a symmetric monoidal category where every tensor composition preserves governance. This allows compositional reasoning about governed programs, with capability-indexed composition bundling machine-checked capability bounds.

A key result is the 'coterminous boundary': every program expressible via four primitive morphism constructors is governed under interpretation, and vice versa. Turing completeness is preserved inside governance, while unmediated I/O is excluded. The framework is parametric—any system instantiating the three axioms inherits all derived properties. Extracted OCaml code runs as a NIF in the BEAM runtime, and property-based testing with 70,000+ random inputs confirmed behavioral equivalence between specification and runtime interpreter with zero disagreements.