Admissible AI Labour Transitions: Minimum Conditions, Uncertainty, and Structural Reopening

Abstract This paper develops an admissibility framework for AI labour transitions in which minimum conditions determine eligibility before economic optimization. It examines material continuity, usable refusal, practical reversibility, credible continuation or re-entry, and reachable revision authority. Their ethical justification and contextual calibration remain separate from the mathematical results. The model distinguishes scattered institutional features from executable routes, individual route availability from joint capacity, and convex feasibility within an arrangement from potentially non-convex choice across arrangements. Under uncertainty, robustly admissible policies must use information available when decisions are made and preserve applicable requirements through evidence production, judgment, and implementation. Safeguards cannot preserve institutional reversibility by exhausting material support or closing other viable pathways. If the complete ordinary robust admissible set is empty, minimizing violation does not restore robust passage. Under unchanged requirements and assessment, restoration requires timely structural reopening. Robust passage, separately justified risk authorization, and unavoidable-breach decisions remain distinct. Within a fixed executable arrangement, stated convexity and regularity conditions support decentralized coordination of shared constraints. Common multipliers or supporting quotas do not alone establish fairness, cooperative efficiency, funding responsibility, or a safe adjustment process. The analysis is theoretical and uncalibrated. Its contribution connects minimum conditions to executable institutional arrangements, effective deadlines, and limited coordination without turning the floor into an objective for unlimited maximization. Research status Working paper, version 0.1 (September 2026). Not peer reviewed. Independent mathematical and applied-ethics review, empirical calibration, and real-world validation have not been completed. AI assistance and research transparency OpenAI ChatGPT was used substantively throughout the research and manuscript-development process, including conceptual and philosophical exploration, mathematical formulation, proposition development, proof and counterexample analysis, literature exploration, drafting and editing, and the development and execution of computational verification software. The reported computational checks evaluate theoretical model configurations. They are not empirical observations and do not constitute independent scholarly review. The verification record distinguishes historical computational results, revised verification runs, and independently implemented computational checks. The minimum ethical conditions and their thresholds require normative justification and contextual calibration; they are not established as universally correct by mathematical proofs or computational testing. The named human author assumes responsibility for the content, cited sources, integrity, and public release of the work.