TSI：用层论框架分析多智能体任务的结构性障碍
Topological Sheaves of Irreducibility: A Theoretical Framework for Multi-Agent Task Obstructions
多智能体系统有些任务卡住不是能力问题，是结构问题。这篇用层论给出可证伪的判定方法，实验数据也给了，适合做 Agent 系统的人看看。
arXiv 论文提出 Topological Sheaves of Irreducibility（TSI），用交互复形 K 和容量层 F 表示任务，以非零上同调类 H^n(K;F) 刻画任务层面的结构性障碍。在 15,625 个 degree-1 输入上，全智能体加性原语可精确完成决策与修复，最优成对系统决策仅 88.80%，仅比 88.79% 的多数类基线高一个输入。在 531,441 个输入的 degree-2 四面体边界任务上，加入四智能体原语后两个任务均变为可精确求解。TSI 提供了任务相关、可证伪的高阶交互检验方法。
Topological Sheaves of Irreducibility: A Theoretical Framework for Multi-Agent Task Obstructions
Multi-agent systems can differ under identical agents and communication budgets when they support different forms of joint interaction. We introduce Topological Sheaves of Irreducibility (TSI), a sheaf-theoretic framework separating task-level compatibility obstructions from system capability. A task is represented by an interaction complex $K$ and a capacity sheaf $\mathcal{F}$; nonzero $H^n(K;\mathcal{F})$ defines a structural signature, while registered interventions test capability. For cocycle data, cochain realization is solvable exactly when the represented cohomology class vanishes. Examples show that the signature is sheaf-relative, and the degree-1 reduction yields cycle-space witnesses and observation requirements. We evaluate two finite one-round models. Across 15,625 degree-1 inputs, an all-agent additive primitive solves decision and repair exactly; the optimal pairwise system reaches 88.80% on decision, one input above the 88.79% majority-class baseline, and 26.63% on repair. On a degree-2 tetrahedral-boundary task over 531,441 inputs, the same-2-skeleton system retains all four three-agent primitives yet matches the pairwise-only optimum throughout the registered separation window, whereas adding the class-filling four-agent primitive makes both tasks exact. Status-preserving robustness checks retain exact performance but are not cost-matched to the class-restoring ablation. Conditional on the registered primitives and cost models, TSI provides task-relative, falsifiable tests of higher-order interaction.
