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Topological Sheaves of Irreducibility: A Theoretical Framework for Multi-Agent Task Obstructions

Steven Motta, Davide Mambelli, Alessandro Rozza · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.26777 · cited by 0 works (OpenAlex) · open-access PDF

Korean

다중 에이전트 레지스트리 시스템은 동일한 에이전트 및 통신 예산에 따라 차이가 있을 수 있습니다. 서로 다른 형태의 공동 상호 작용을 지원할 때. 우리는 작업 수준의 호환성 장애를 시스템 능력으로부터 분리하는 작업 이론적 프레임 워크 (TSI)를 소개합니다. 작업은 상호 작용 복잡 $K$ 및 용량 셰프 $\mathcal{F}$에 의해 표현됩니다. 예제는 서명이 sheaf-relative이며, 단계 1 단계는 작업 공간과 관찰 요구 사항이 동일한 구조 서명을 정의합니다. 코치클 데이터의 경우, cochain 실현은 대표되는 cohomology 클래스가 사라질 때 정확하게 해결할 수 있습니다. 예제는 서명이 sheaf-relative이며, 단계 1

Machine translation (Meta M2M100); the English original follows.

Abstract

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.

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Topics: Mathematics, Irreducibility, Pairwise comparison, Robustness (evolution), Topology (electrical circuits), Affine transformation

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