From Graph Neural Networks to Sheaf Neural Networks. We evolved past GNNs to build AI agents grounded in H⁰ Cohomology — the mathematics of verified truth.
Topos Agents calculate a Holonomy Defect. If the math doesn't add up, the AI knows it is confused, preventing confident hallucinations.
When confusion persists, the system evolves. It dynamically expands its "Commitment Modality" to incorporate new logic at runtime.
Static firewalls fail. Topos Agents learn from attack patterns in real-time, rewriting their own defense logic to block new exploits.
We started with Graphormer (GNN) as a proof-of-concept. Then we realized: standard GNNs lose information at boundaries. Sheaf Neural Networks preserve it — using H⁰ Cohomology to guarantee global consistency from local agent observations.
Trust signals propagate via Laplacian diffusion on the Sheaf. Replaces naive message-passing with topology-aware learning.
Global sections of the Sheaf define consensus. If local observations don't glue, the defect is detected — mathematically, not heuristically.
Sheaf Laplacian computed at hardware speed via vectorized native operations. 30K+ topological verifications per second.
Watch as the Topos Agent encounters a malicious transaction that follows code rules but violates topological intent.
Read the full technical report or download the Dynamis Kit to build your own agents.