

















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).
| Comments: | 17 pages, 2 figures. Companion proofs: this https URL. Project: this https URL. v2: corrected cross-reference identifiers for companion papers;updated license |
| Subjects: | Artificial Intelligence (cs.AI) |
| ACM classes: | D.2.4; D.3.1; I.2.0 |
| Cite as: | arXiv:2604.27292 [cs.AI] |
| (or arXiv:2604.27292v3 [cs.AI] for this version) | |
| https://doi.org/10.48550/arXiv.2604.27292 arXiv-issued DOI via DataCite |
From: Alan McCann [view email]
[v1]
Thu, 30 Apr 2026 01:12:32 UTC (24 KB)
[v2]
Tue, 5 May 2026 10:43:57 UTC (22 KB)
[v3]
Tue, 26 May 2026 12:26:33 UTC (22 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。