Formal Proofs Verify Machine Governance in AI Systems
McCann's mechanized theory establishes mathematical foundations for controlling intelligent systems through coinductive safety predicates and verified interpreter specifications.
McCann proves five theorems about structural governance for intelligent systems, with three mechanized in Coq and two on paper, plus a verified runtime specification.
- — Coinductive Safety Predicate (gov_safe) captures governance safety for infinite program behaviors using boolean permission flags.
- — Governance Invariance Theorem shows governance properties hold uniformly across meta-recursive levels by definitional equality.
- — Four atomic primitives (code, reason, memory, call) are expressively complete for any discrete intelligent system.
- — Alternating Normal Form decomposes machines into canonical alternating code and effect layers with confluent rewriting.
- — Necessity Theorem proves the reason primitive is mathematically required for semantic judgment problems via Rice's theorem reduction.
- — Verified Interpreter Specification formalizes BEAM runtime trust and capability logic, tested against 70,000+ generated sequences with zero disagreements.
- — Mechanization spans 12,000 lines across 36 Coq modules with 454 theorems and zero admitted lemmas.
Astrobobo tool mapping
- Knowledge Capture Document the five theorems and their practical implications in a structured note: which apply to your system, which require further work, which are already implicit in your design.
- Reading Queue Queue the full paper and the Coq mechanization repository (if public) for deep study; prioritize the Verified Interpreter Specification section for immediate relevance.
- Focus Brief Prepare a one-page summary of how formal governance applies to your organization's AI systems: what would need to be formalized, what tooling gaps exist, what regulatory value it would provide.
Frequently asked
- The Coinductive Safety Predicate (gov_safe) is a mathematical property that captures whether an intelligent system's behavior remains governed across infinite execution. It uses a boolean permission flag that is provably false for ungoverned input/output and true for governed interpretations. This matters because it provides a formal, machine-checkable definition of governance that holds for systems that run indefinitely, not just finite programs.
cite ▸
APA
Alan L. McCann. (2026, May 2). Formal Proofs Verify Machine Governance in AI Systems. Astrobobo Content Engine (rewrite of arxiv/cs.AI). https://astrobobo-content-engine.vercel.app/article/formal-proofs-verify-machine-governance-in-ai-systems-a1492a
MLA
Alan L. McCann. "Formal Proofs Verify Machine Governance in AI Systems." Astrobobo Content Engine, 2 May 2026, https://astrobobo-content-engine.vercel.app/article/formal-proofs-verify-machine-governance-in-ai-systems-a1492a. Based on "arxiv/cs.AI", https://arxiv.org/abs/2604.27289.
BibTeX
@misc{astrobobo_formal-proofs-verify-machine-governance-in-ai-systems-a1492a_2026,
author = {Alan L. McCann},
title = {Formal Proofs Verify Machine Governance in AI Systems},
year = {2026},
url = {https://astrobobo-content-engine.vercel.app/article/formal-proofs-verify-machine-governance-in-ai-systems-a1492a},
note = {Astrobobo rewrite of arxiv/cs.AI, https://arxiv.org/abs/2604.27289},
}