Implementing Computational Law in Wolfram Language for the Governance of Artificial Intelligence

We present a machine-checked formalization of structurally governed AI workflow architectures and prove that effect-level governance can be imposed without reducing internal computational expressivity. Using Interaction Trees in Rocq 8.19, we define a governance operator G that mediates all effectful directives, including memory access, external calls, and oracle (LLM) queries. Our development compiles with 0 admitted lemmas and consists of 36 modules, ~12,000 lines of Rocq, and 454 theorems. We establishseven properties: (P1) governed Turing completeness, (P2) governed oracle expressivity, (P3) a decidability boundary in which governance predicates are total and closed under Boolean composition while semantic program properties remain non-trivial and undecidable by governance, (P4) goal preservation for permitted executions, (P5) expressive minimality of primitive capabilities (compute, memory, reasoning, external call, observability), (P6) subsumption asymmetry showing structural governance strictly subsumes content-level filtering, and (P7) semantic transparency: on all executions where governance permits, the governed interpretation is observationally equivalent (modulo governance-only events) to the ungoverned interpretation. Together, these results show that governance and computational expressivity are orthogonal dimensions: governance constrains the effect boundary of programs while remaining semantically transparent to internal computation.

Legal texts often contain computational legal clauses--provisions whose understanding requires complex logic. While frontier Large Reasoning Models (LRMs) can describe such clauses, building production-ready systems is limited by reasoning errors and the high cost of inference. We propose Amortized Intelligence, a neuro-symbolic approach where we use an LLM once to translate a legal text into Deterministic Autonomous Contract Language (DACL): a typed graph intermediate representation. Adjudication then relies on deterministic graph executions with a visually auditable trace. In comparison against runtime LRM baselines (including GPT-5.2 and Gemini 3 Pro), our DACL-based Agent achieves near-perfect consistency and mitigates the "reasoning cliff" observed in probabilistic models. The system reduces compute costs by over 90% in high-volume workflows while satisfying the strict auditability requirements of legal adjudication.

Every system that performs effects has two boundaries: what it can do (expressiveness) and what governance covers (governance). In nearly all deployed AI systems, these boundaries are defined independently, creating three regions: governed capabilities (the only useful region), ungoverned capabilities (risk), and governance policies that address non-existent capabilities (theater). Two of the three regions are failure modes. We focus on the governance of effects: actions that AI systems perform in the world (API calls, database writes, tool invocations). This is distinct from the governance of model outputs (content quality, bias, fairness), which operates at a different level and requires different mechanisms. We present a formal framework for analyzing this structural gap. Rice's theorem (1953) proves the gap is undecidable in the general case for any Turing-complete architecture that attempts to govern effects behaviorally: no algorithm can decide non-trivial semantic properties of arbitrary programs, including the property "this program's effects comply with the governance policy." We define coterminous governance: a system property where the expressivenessboundary equals the governance boundary. We show that coterminous governance requires an architectural decision (separatingcomputation from effect) rather than a governance layer added after the fact. We show that structural governance under this separation subsumes separate governance infrastructure: governance checks become part of the execution pipeline rather than a second system running alongside it. We propose coterminous governance as the testable criterion for any AI governance system: either the two boundaries are provably identical, or risk and theater are structurally inevitable. Proofs are mechanized in Coq (454 theorems, 36 modules, 0 admitted).