sheaf-theoretic-coordination

What problem does it solve?

This Skill provides sheaf-theoretic coordination mechanisms for distributed agents, enabling consensus via a sheaf Laplacian, inference via harmonic extension, and global consistency checks via cohomology.

Core Features & Use Cases

• Sheaf Laplacian: Distributed consensus dynamics on a cellular sheaf.
• Harmonic Extension: Global inference under partial observations.
• Cohomology Detection: Identify global obstructions to agreement.
• Sheaf Neural Networks: Learn and diffusion-layer parameters from data.
• Use Case: Coordinating robotic swarms or sensor networks with topological constraints.

Quick Start

Build a cellular/sheaf over a base complex, initialize restriction maps, and run diffusion or harmonic extension to obtain a consistent global state.