Sheaf-Theoretic Transport and Obstruction for Detecting Scientific Theory Shift in AI Agents

基于层论（Sheaf-Theoretic）的迁移与阻碍：用于检测人工智能体中的科学理论范式转移

Abstract: Scientific theory shift in AI agents requires more than fitting equations to data. An artificial scientific agent must detect whether an existing representational framework remains transportable into a new regime, or whether its language has become locally-to-globally obstructed and must be extended.

摘要： 人工智能体中的科学理论范式转移不仅仅是方程对数据的拟合。一个人工智能科学体必须能够检测现有的表征框架是否仍然可以迁移到新的领域，或者其语言是否在局部到全局的层面上产生了“阻碍”（obstructed），从而必须进行扩展。

This paper develops a finite sheaf-theoretic framework for detecting theory-shift candidates through transport and obstruction. Contexts are organized as a local-to-global structure in which source, overlap, target, and validation charts are fitted, restricted, and tested for gluing.

本文开发了一个有限层论框架，通过“迁移”和“阻碍”来检测理论转移的候选方案。我们将语境组织为一种局部到全局的结构，其中源图表、重叠图表、目标图表和验证图表被进行拟合、限制，并测试其是否满足“粘合”（gluing）条件。

Obstruction measures failure of coherence through residual fit, overlap incompatibility, constraint violation, limiting-relation failure, and representational cost. We evaluate the framework on a controlled transition-card benchmark designed to separate deformation within a source language from extension of that language.

“阻碍”通过残差拟合、重叠不兼容性、约束违规、极限关系失效以及表征成本来衡量一致性的缺失。我们在一个受控的“转换卡”基准测试上评估了该框架，该基准旨在区分源语言内部的变形与该语言的扩展。

The main result is direct obstruction ranking: the intended deformation or extension is usually the lowest-obstruction candidate, and transition type is separated in the benchmark. A constellation kernel over the same signatures is included only as a secondary representational-similarity probe.

主要研究结果是直接的阻碍排序：预期的变形或扩展通常是阻碍程度最低的候选方案，且转换类型在基准测试中得到了有效区分。文中包含了一个基于相同签名的星座核（constellation kernel），仅作为辅助性的表征相似度探测手段。

The aim is not to reconstruct historical paradigm shifts or solve open-ended autonomous theory invention, but to isolate a finite diagnostic subproblem for AI agents: detecting when representational transport fails and extension becomes the coherent next move.

本研究的目的并非重构历史上的范式转移或解决开放式的自主理论发明，而是为人工智能体分离出一个有限的诊断子问题：即检测表征迁移何时失效，以及何时进行扩展才是逻辑上连贯的下一步行动。