Module graph 

Fleet Constraint Graph — Laman Rigidity + H¹ Cohomology

Laman’s theorem (1867): A graph with V vertices is generically rigid in 2D iff it has exactly 2V-3 edges and every subgraph with v’ vertices has at most 2v’-3 edges.

Key caveat: Laman’s theorem establishes the edge count condition (E=2V-3 for generic rigidity in 2D) and the subgraph condition (every subgraph has at most 2v’-3 edges), but does NOT place an upper bound on vertex degree. A Laman graph can have vertices of arbitrarily high degree.

This maps directly to fleet coordination:

• Vertices = agents
• Edges = trust/communication links
• Rigid graph = provably self-coordinating fleet (no central coordinator)

H¹ dimension = number of independent cycles = number of redundant constraint paths = “emergence” in the network.

Structs

FleetAgent

One agent in the fleet

FleetGraph

The fleet constraint graph

RigidityResult

Result of rigidity analysis