Doctrine as a Fixed Point: A Formal Model of the Enforceable Penalty Ceiling when Human Oversight of AI Must Remain Effective

Abstract

Article 14 of the EU AI Act requires that a high-risk system be overseen by natural persons who understand its limits, remain alert to automation bias, and can disregard or override its output. That capability is invisible in the output and decays precisely when the system is good. A provider can certify it only by an outcome-contingent liability commitment, and how large a commitment courts will enforce is itself open. After Cavendish the enforceable multiple of actual loss is measured against the legitimate interest the clause protects; where that interest is preserved oversight capability, it exists only if the market separates, which requires a sufficiently permissive doctrine. We model the enforceable ceiling as a fixed point of an expectations map on a complete lattice. Existence follows from Knaster-Tarski. Because no case separates at compensation, compensation is always an equilibrium; once the doctrinal uplift clears a threshold set by the case population, a permissive equilibrium and a watershed appear, and the map inherits the provider's solvency cap, so an insurance withdrawal deep enough and long enough can destroy the permissive equilibrium, which returning cover does not restore. Perturbing the adjustment yields a closed-form long-run tipping point, exact recovery times, and the noise levels at which irreversibility fails. The welfare cost of the resulting trap is capped at the drafting cost of primary-obligation substitutes. The order-theoretic core is machine-checked in Lean 4 with an axiom-free report. Both AI-side parameters, shared-base-model intensity and provability, are matched to instruments available in 2026.