sheaf-laplacian-coordination

Name: sheaf-laplacian-coordination
Availability: InStock
Author: plurigrid

Solve distributed consensus and harmonic inference with sheaf Laplacian coordination.

60|13|Updated Dec 22, 2025

Search Tags:#consensus #distributed #cohomology #laplacian #harmonic-extension #sheaf

Ready to run

npx skills add https://github.com/plurigrid/asi --skill sheaf-laplacian-coordination

💬 Prompt for ChatGPT / Claude Chat▼

Please help me install this Agent Skill.
Skill: sheaf-laplacian-coordination
Source: https://github.com/plurigrid/asi/tree/main/ies/music-topos/.ruler/skills/sheaf-laplacian-coordination
Command: npx skills add https://github.com/plurigrid/asi --skill sheaf-laplacian-coordination

SYSTEM DOCUMENTATION & REQUIREMENTS

💡 This Skill requires Catlab.jl.

What problem does it solve?

This Skill provides distributed coordination for multi-agent systems by modeling interactions as a cellular sheaf and using a graph Laplacian to drive consensus and inference across agents.

Core Features & Use Cases

Sheaf Laplacian: Consensus dynamics on the sheaf to reach agreement among agents.
Harmonic Extension: Infer missing data via globally consistent assignments.
Cohomology Detection: Identify obstructions to global agreement.
Sheaf Neural Networks: Learn restriction maps and diffusion layers from data.
Use Case: Swarm robotics or sensor networks where only partial observations are available.

Quick Start

Build a CellularSheaf over your network, define stalks and restrictions, then run diffusion or harmonic extension to reach consensus.

Frequently Asked Questions about sheaf-laplacian-coordination

High-intent search queries and answers about installing and using this skill.

FAQPage Schema

How do I coordinate multi-agent consensus using sheaf Laplacians?▼

Sheaf Laplacian coordination models agent interactions as a cellular sheaf over a graph, then applies Laplacian diffusion to drive consensus. Build a CellularSheaf with stalks for each agent, define restriction maps per edge, and run diffusion dynamics to reach distributed agreement across your network.

What is harmonic extension and when do I use it in distributed systems?▼

Harmonic extension infers globally consistent assignments for missing or partial observations in a network by solving a harmonic condition on the sheaf. Use it when you have partial data from sensors or agents and need to reconstruct missing values while respecting the network's structural constraints.

Can I detect obstructions to consensus in multi-agent systems?▼

Yes, cohomology detection identifies obstructions to global agreement by analyzing the sheaf structure. These obstructions reveal fundamental limitations preventing all agents from reaching consensus, helping you diagnose why coordination fails.

How do I build learnable sheaf neural networks for multi-agent coordination?▼

Sheaf neural networks learn restriction maps and diffusion layers directly from data using Catlab.jl. Define stalks as vector-valued representations per agent, parameterize restriction maps as learnable functions per edge, and train end-to-end on coordination or inference tasks.

What are the prerequisites before applying sheaf Laplacian methods to my network?▼

You need to represent your multi-agent system as a directed or undirected graph with vector-valued stalks per node and define or learn restriction maps per edge. Catlab.jl must be available for constructing the cellular sheaf and Laplacian operators.

Does this approach work for swarm robotics and sensor networks?▼

Yes, sheaf Laplacian coordination is designed for swarm robotics and sensor networks where agents have partial observations. It handles vector-valued state representations and distributed consensus across heterogeneous network topologies.