Algebraic Semantics for Governed Execution in Monoidal Categories

A recent paper published on arXiv introduces an algebraic semantics for governed execution, framing governance as both compositional and coterminous with expressibility. This framework is implemented through 32 Rocq modules, comprising around 12,000 lines of code, which include 454 theorems and no accepted proofs. It utilizes interaction trees and parameterized coinduction. A GovernanceAlgebra record, defined by three axioms—safety, transparency, and properness—creates a symmetric monoidal category, verified for pentagon, triangle, and hexagon coherence, ensuring governance is maintained in every tensor composition. An algebraic effect system limits the handler algebra, allowing only governance-preserving handlers in the safe fragment; programs within the empty capability set can only produce observability directives. Capability-indexed composition integrates programs with machine-verified capability limits, and a dual guarantee theorem confirms that within_caps and gov_safe are upheld across all composition operators.