本体论自由意志作为不可压缩信息的附加：超越P与NP问题的不可计算性边界

中文摘要 AI 辅助

我们研究了一个本体论自由意志的条件模型，在该模型中，前行动状态构建了若干连贯的全局延续，而并未在本质上区分其中哪一个将成为未来的现实化。拓扑斯理论部分通过选择层以及保持前行动数据的自同构作用来形式化：不动点的缺失排除了任何自然的等变选择。一个行动将无指向对象变为有指向对象，并将其对称群简化为稳定子群。独立地，一个因果算法不可压缩性公理对实际选择施加了近乎最大的在线描述复杂性。随后，一致可观测的行动后痕迹允许对其重构。我们证明了一个条件转移结果：此类痕迹必须渐近地携带所有在前行动体制中不可用的奇异化信息，并且没有统一的图灵预测器能仅凭因果历史计算这些选择。该形式体系既未证明人类满足该模型，也未证明P与NP的分离；它确定了一个边界，在此边界上，预测关注的是可计算函数的存在性，而非其时间复杂性。

英文摘要

We study a conditional model of ontological free will in which a pre-act state structures several coherent global continuations without intrinsically distinguishing one as the future actualisation. The topos-theoretic component is formalised by a choice sheaf and by the action of automorphisms preserving the pre-act data: the absence of a fixed point rules out any natural equivariant selection. An act changes an unpointed object into a pointed one and reduces its symmetry group to a stabiliser. Independently, a causal algorithmic incompressibility axiom imposes nearly maximal online description complexity on the actual choices. Uniformly observable post-act traces then allow their reconstruction. We prove a conditional transfer result: such traces must carry asymptotically all the singularisation information unavailable in the pre-act regime, and no uniform Turing predictor computes the choices from causal histories alone. The formalism proves neither that human beings satisfy the model nor a separation of P from NP; it identifies a boundary at which prediction concerns the existence of a computable function rather than its time complexity.

发表机构

• French Air and Space Force（法国空军和太空军）
• Centre for Aerospace Strategic Studies (CESA)（航空航天战略研究中心）
• Paris School of International Affairs (PSIA), Sciences Po（巴黎政治学院国际事务学院）

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