AI 中文总结
该研究提出预测器不可能性定理（PITT），构建阶段语言层级，定义聚合语言MIS并证明其属于NP\backslash P，为有效预测器族的存在性提供桥梁定理，方法不具相对性、代数化或自然化性质。
AI 中文摘要
我们引入了由语义算子生成的阶段机、阶段域和阶段语言构成的层级结构。核心结果是预测器不可能性定理（PITT），该定理表明，不存在任何有效预测器族能够统一判定此层级中的所有阶段语言。证明过程利用伪补构造得到一种语言，该语言与P中的每一种语言都产生矛盾。随后，我们定义聚合语言MIS，并建立将聚合输入与单个阶段语言关联的形式化切片定理，这为从MIS的多项式时间可判定性到有效预测器族存在性提供了严格的桥梁定理。通过利用简洁表示，该聚合语言被证明在确定性多项式时间内不可判定；在定义有效聚合对象的聚合增长条件下，MIS属于NP类。结合这两个结果得到主定理：MIS属于NP\backslash P。本文的组织结构使得PITT可作为独立理论结果存在，而复杂性理论推论则从聚合语言框架导出。该方法不具有相对性、代数化或自然化性质。
英文摘要
We introduce a hierarchy consisting of stage machines, stage domains, and stage languages generated by semantic operators. The central result is a Predictor Impossibility Theorem (PITT), which shows that no effective predictor family can uniformly determine all stage languages of our hierarchy. The proof makes use of a pseudo-complement construction to obtain a language that yields a contradiction with every language in P. We then define an aggregate language MIS and establish a formal Slice Theorem connecting aggregate inputs to individual stage languages. This provides a rigorous Bridge Theorem from polynomial-time decidability of MIS to the existence of an effective predictor family. By utilizing succinct representations, the aggregate language is shown to be undecidable in deterministic polynomial time. Under the aggregate growth condition defining valid aggregate objects, MIS is shown to belong to NP. Combining these two results yields our main theorem: MIS in NP setminus P. The paper is organized so that PITT stands independently as a theoretic result, while the complexity-theoretic consequences are derived from the aggregate-language framework. The method does not relativize, algebrize, or naturalize.
Comments4 pages plus 2 page Appendix which includes non-relativization, non-algebrization, and non-naturalization results. This paper is a simplified and improved version of arxiv.org/abs/2607.06956, submitted on 07/06/2026, which did not include the barrier-crossing Appendix
