What question did this study set out to answer?

This research aims to establish a framework for deterministic authorization to close the authorization gap in autonomous AI systems.

May 28, 2026Open Access

The Lakhowal Law of Concurrence: A Deterministic Authorization Primitive for Runtime AI Governance with Hardware-Rooted Closure and Paired Falsification Surfaces

Key Points

This research aims to establish a framework for deterministic authorization to close the authorization gap in autonomous AI systems.
Developed the Lakhowal Law of Concurrence with eight foundational theorems
Utilized linear temporal logic for formalizing safety invariants
Mechanically verified the framework using TLA+ and the TLC model checker
Establishes deterministic authorization that ensures safety predicates evaluate to one.
Introduces verification frameworks that provide convergent perspectives on safety invariance.
Demonstrates the framework's adaptability across various hardware architectures.

Abstract

This paper introduces the Lakhowal Law of Concurrence (LLC), a deterministic authorization primitive for runtime AI governance at the action-execution boundary. The framework addresses the authorization gap in autonomous AI systems by requiring non-compensatory concurrence across every safety predicate before an externally effective action is permitted: a permit is issued only when every individual deficit is zero, equivalently when every predicate evaluates to one. No compensatory aggregation — no weighted sum, no quorum threshold — can substitute. Eight foundational theorems establish deterministic authorization, fail-closed composition, non-compensatory soundness, non-bypassability under three-signal hardware closure, replay closure, model-substitution invariance, TOCTOU state-consistency, and composite conservation stability. The global safety invariant is formalized in linear temporal logic and mechanically verified in TLA+ (ConcurrenceCore module) by the TLC model checker, with extension to the unbounded deployment model by inductive-invariant argument. The primitive is substrate-neutral and admits hardware-rooted (Tier-H), TEE-rooted (Tier-T), software-only (Tier-S), distributed-quorum (Tier-D), and cross-tier (Tier-X) realizations, with a formal assurance ladder enumerating which authorization properties are fully guaranteed, degraded, or structurally absent at each tier. The paper also introduces eight paired falsification surfaces committed in advance on the public record, eight convergent verification frameworks observing the same invariant from independent epistemic vantages, and explicit bridges to the companion enforcement architecture (L-DREA), the Execution Integrity construct submitted to NIST AI 800-2, and the ConcurBench v1. 0 reproducibility benchmark. Companion artifact: https: //github. com/AGLakhowal/Gamma-Permit-Package Companion architecture paper: Gill, A. , "Deterministic Runtime Enforcement for Autonomous AI Agents: A Substrate-Neutral Reference Monitor for the Execution Boundary, " IEEE Access (under review), May 2026. Patent priority: U. S. Patent Application Publication No. US 2026/0127298 A1, filed November 10, 2025. Eight-application USPTO portfolio. FRAND commitment on record (see Appendix C of the paper).

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