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 w...
| Authors | Steven Motta, Davide Mambelli, Alessandro Rozza |
|---|---|
| Primary category | cs.LG |
| Published | 19 October 2026 |
| Last updated at source | 19 October 2026 |
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