局部验证无法检测不可迁移性：智能体推理中上下文保持的上同调理论
Local verification cannot detect non-transportability: a cohomological theory of context preservation in agentic reasoning
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中文总结 AI 辅助
本文提出智能体推理上下文保持的上同调理论，证明局部验证无法检测不可迁移性，提出Ksetra方法并通过外汇市场验证了所提检验的有效性。
中文摘要 AI 辅助
智能体AI系统常将结论迁移至生物、临床及金融等不同上下文场景，新兴的安全防护手段是局部验证：在每一步检查实体是否可在所选工具中表示、参数是否兼容、输出是否与计划一致。本文证明这类安全防护手段在结构上是不完备的。通过将上下文空间建模为其神经丛、证据建模为实值1-上链，智能体对证据的链式推理执行路径积分：当且仅当上链是恰当的，其结论与路径无关；有效推理路径间的分歧恰好是第一Cech上同调类的和乐。Hodge分解将证据冲突划分为梯度部分（校准）、旋度部分（局部不一致，在三重重叠处可见）及调和部分。本文核心结果是：没有任何单纯形支撑的一致性检查族能区分ω与ω+h（其中h为调和项），但后者会在有效路径间产生非零分歧；检测需基于循环基的统计量。由此得到的过程Ksetra通过上边缘投影进行估计，并基于调和分量触发弃权（不执行），本文给出其机制：该机制源于效应修饰结合重叠特定的总体构成，当不存在效应修饰时，该机制会消失至机器精度。证据网络的自由度被划分为校准、一致性及可迁移性，从而产生全局断言存在性的精确F检验；本文量化了其在精度不均时的失真，并提供恢复精确性的精度白化形式。外汇市场作为校准基准，其无套利零假设使上链恰好为上边缘，该检验尺寸正确，可检测循环套利，且忽略三角套利。
英文摘要
Agentic AI systems routinely transport conclusions across biological, clinical and financial contexts, and the emerging safeguard is local verification: checking at each step that the entity is representable in the chosen tool, that parameters are compatible, and that outputs cohere with the plan. We prove this class of safeguard is structurally incomplete. Modelling a covering of context space by its nerve and evidence by a real-valued 1-cochain, an agent chaining evidence performs path integration: its conclusion is path-independent if and only if the cochain is exact, and disagreement between valid reasoning paths is exactly the holonomy of a first Cech cohomology class. Hodge decomposition partitions evidence conflict into a gradient part (calibration), a curl part (local inconsistency, visible at triple overlaps) and a harmonic part. Our central result is that no family of simplex-supported consistency checks can distinguish omega from omega+h for harmonic h, which nonetheless generates non-zero disagreement between valid paths; detection requires a statistic on a cycle basis. The resulting procedure, Ksetra, estimates by coboundary projection and gates abstention on the harmonic component, which we give a mechanism: it arises from effect modification combined with overlap-specific population composition, and vanishes to machine precision when effect modification is absent. The degrees of freedom of an evidence network partition into calibration, coherence and transport, yielding an exact F-test for the existence of a global claim; we quantify its distortion under unequal precision and supply the precision-whitened form that restores exactness. Foreign exchange, where the arbitrage-free null makes the cochain exactly a coboundary, serves as a calibration bench: the test is correctly sized, fires on loop arbitrage, and ignores triangular arbitrage.
