The Two Boundaries: Why Behavioral AI Governance Fails Structurally
- URL: http://arxiv.org/abs/2604.27292v1
- Date: Thu, 30 Apr 2026 01:12:32 GMT
- Title: The Two Boundaries: Why Behavioral AI Governance Fails Structurally
- Abstract summary: We focus on the governance of effects, actions that AI systems perform in the world.<n>Rice's theorem proves the gap is undecidable in the general case for Turing-complete architecture.<n>We propose coterminous governance as the testable criterion for any AI governance system.
- Score: 0.0
- License: http://creativecommons.org/publicdomain/zero/1.0/
- Abstract: 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).
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