Holonomic Information Management: Sheaf-Theoretic Navigation of Arrovian Possibility

This paper presents a novel framework to formalize organizational information and decision-making as a patching problem of local preference sections within a sheaf. The fundamental challenge of information management is identified as patching failure: Arrovian Impossibility means a topological obstruction where the assembled preferences of agents—including managers, workers, experts, and AIs—are forced to choose between global obstructions (dictatorship) or local obstructions (intransitivity). By clarifying the holonomic requirements to coordinate local interactions, this framework restores ‘Arrovian Possibility’ within the subspace where global structural obstructions are formally neutralized. By applying Čech cohomology, we provide a navigational methodology to identify and excise these singularities, thereby restoring global consistency. Computational experiments across various scenarios reveal a small number of maximal consistent regimes, all uniquely associated with a specific governance rule. Notably, the ratio of maximal consistent domain size to total profiles is relatively large in all cases (e.g., 85.0% for \((n, m) = (2, 5)\) ), suggesting that, assuming a coarse-grained modeling, there always exists a structurally stable design space to be established.