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C-HD: AI-Discovered Shortest-Path Algorithm

Vals AI

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Sep 22, 2026

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Ten Claude Opus 5.5 agents collaborated for 15 hours to devise C-HD, a new shortest-path algorithm that formally beats published bounds — then proved it correct in Lean. The visualization shows a weighted grid where each cell carries a directional arrow, with the optimal C-HD route traced in dark green from origin circle to destination pin. It's a genuine research artifact: a machine-discovered, machine-verified improvement over decades of human-authored graph theory.

Ten agents running in parallel produced a formally verified algorithm improvement in just 15 hours
The Lean proof means the result is mathematically guaranteed, not just empirically tested
C-HD improves on published complexity bounds for shortest-path — a result that eluded human researchers

“We asked ten Claude Opus 5.5 agents to devise a faster shortest-path algorithm and prove it in Lean. Within 15 hours, they produced C-HD: a formally verified improvement over the published bounds.”
— @ValsAI

graph-algorithms formal-verification lean-proof multi-agent research algorithm-discovery minimal light