AI 中文总结
本文研究专家服务市场中责任承诺的可执行倍数如何内生决定，证明教义映射存在多重不动点，并揭示资本冲击导致不可逆崩溃及制度极化。
AI 中文摘要
在人工智能不断改进的专家服务市场中，通过基于结果的责任承诺来实现分离，只有当可执行的实际损失倍数 $m$ 足够大时才能成立。该领域文献（包括我们自己的研究）将 $m$ 视为法律给定数据，但事实并非如此。在Cavendish案之后，可执行倍数需对照条款所保护的合法利益来衡量；当该利益是保留人类后备能力时，该利益仅在承诺能够实现分离时才存在，而这又要求 $m$ 足够大。我们闭合了这一循环，并研究由此产生的教义映射 $m' = D(m)$。我们得出六项结果。第一，$D$ 在完备格上是单调的，因此存在不动点，且除非最大教义提升超过案件层面阈值离散度的四倍，否则该不动点是唯一的；当出现多重性时，通常存在三个不动点，其中外侧两个是稳定的。第二，基于主要法律来源的校准得出一个分类：美国和协商性德国B2B合同属于确定性制度；英格兰以及（自BPL诉Morgan Securities案（2025）以来）印度属于多重性制度，其分水岭为1.95。第三，教义映射继承了偿付能力上限，因此当偿付能力比率跨越分水岭时，均衡上限出现不连续，下降0.92。第四，这种崩溃是不可逆的：恢复能力并不能恢复教义；在内生教义下，配套论文的制度映射发生极化，其中间单元消失。第五，特质性噪声使得长期教义变得唯一，并在教义范围的中点处给出一个闭合形式的临界点，该临界点与离散度无关；不可逆性变为亚稳态，具有Kramers指数恢复时间。第六，序理论核心已在Lean 4中通过机器验证，公理报告为无。
英文摘要
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.
Comments35 pages, 6 figures, 5 tables. Final version; Companion papers: arXiv:2607.26327 (Games 17(5), 49), arXiv:2608.04276, arXiv:2608.05969, arXiv:2609.26141. Order-theoretic core in Lean 4. Replication package: https://doi.org/10.6084/m9.figshare.33212916 . Explorer: https://tafew.github.io/doctrine-fixed-point/
