The Two Boundaries: Why Behavioral AI Governance Fails Structurally

Researchers present a formal framework proving that AI governance systems structurally fail when expressiveness boundaries (what AI can do) and governance boundaries (what's regulated) are defined independently, creating inevitable gaps. The paper proposes 'coterminous governance'—aligning these boundaries through architectural separation of computation from effects—as the only viable solution, with proofs mechanized in Coq.

This paper addresses a fundamental structural problem in AI governance that has eluded industry solutions: the inherent mismatch between what AI systems can technically accomplish and what governance frameworks actually regulate. Researchers demonstrate that Rice's theorem guarantees this gap is mathematically undecidable for Turing-complete systems attempting behavioral governance, meaning no algorithm can verify whether arbitrary program effects comply with policies. This creates three inevitable regions—governed capabilities (useful), ungoverned capabilities (risk), and theater (policies addressing non-existent capabilities)—with two constituting failure modes.

The work distinguishes AI effects governance (actions in the world like API calls and database writes) from output governance (bias, fairness, content quality), recognizing these require different mechanisms. Current deployed systems treat governance as an overlay rather than architectural constraint, perpetuating structural vulnerabilities. The authors propose coterminous governance as a testable criterion: expressiveness and governance boundaries must be provably identical through architectural design separating computation from effects execution. This reframes governance from a policy layer into an execution pipeline component.

For the AI and cryptocurrency industries, this framework carries significant implications. Projects claiming robust AI governance without architectural separation between computation and effects lack mathematical guarantees against failure modes. In DeFi and autonomous systems relying on AI decision-making, ungoverned capabilities represent material operational risk. The mechanized proofs in Coq (454 theorems, 36 modules) provide formal verification credibility. Organizations deploying AI systems should evaluate whether governance boundaries align architecturally with expressiveness, not merely administratively. This research establishes empirical criteria for distinguishing genuine governance from theater—critical for regulatory compliance, institutional adoption, and investor confidence in AI-driven systems.

• →AI governance fails structurally when expressiveness and governance boundaries are defined independently, creating mathematically inevitable risk zones.
• →Rice's theorem proves behavioral effect governance is undecidable for Turing-complete systems, making algorithmic compliance verification impossible.
• →Current governance layers fail because they operate as separate systems rather than architectural constraints on computation-effect separation.
• →Coterminous governance requires architectural redesign separating computation from effects execution, not policy additions to existing systems.
• →Mechanized proofs in Coq provide formal verification criteria to distinguish genuine AI governance from regulatory theater.