Watch this space

Watch the Space for Governed Swarms Of Agents, with Finality.

• Paper
• Scissors
• Stone
• Well

A sheaf is a rule of agreement: to every place, a local datum; to every overlap, a restriction map that says how those data must coincide. A global section is not unanimity. It is an assignment that is consistent exactly where the parts actually meet.

That is why a sheaf is a viable object for coordinating agents. Agents do not share one scalar state. They observe different subspaces of the evidence. Classical consensus pretends otherwise and then fights the remainder as noise. A cellular sheaf keeps each role’s stalk intact and measures disagreement only on the shared restriction. Diffusion on the sheaf Laplacian drives that disagreement — the Dirichlet energy — toward zero. Finality on this layer is reaching a global section: the swarm has not merely scored well; the roles agree on what they jointly see.