10 Claude Opus 5.5 agents prove faster shortest-path algorithm in Lean within 15 hours
ricklamers · x · 2026-09-23
vals.ai tasked 10 Claude Opus 5.5 agents with finding a faster shortest-path algorithm and proving it in Lean via a shared message board. After 15 hours and 733 messages, they produced C-HD: a formally verified improvement over the published bounds.
- Setup: directed graph, non-negative real weights, exact answers, internal operations counted toward runtime. Dijkstra runs in O(m+n log n); a 2025 breakthrough gives O(m log^(2/3) n), but Dijkstra still wins across a broad region of the parameter space
- Method: the swarm split work, debated, and iterated proofs on a multi-agent message board
- Takeaway: a concrete advance showing frontier model swarms pushing into serious mathematical research and machine-checked proofs
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