Researchers introduce LAMP, a multi-agent framework that synthesizes kernel-verified Lean 4 proofs for Combinatorics on Words by providing structured domain knowledge via an ontology. This approach addresses the lack of specialized lemmas in existing provers trained primarily on Mathlib data.
- The authors present a new Lean 4 formalization of Combinatorics on Words containing eight modules and 93 declarations of core definitions and foundational lemmas.
- LAMP coordinates a Planner, Builder, and Verifier using Model Context Protocol access to the domain-specific ontology without requiring prover fine-tuning.
- In tests across 90 theorems spanning three difficulty levels, LAMP synthesized verified proofs for 96.7% of cases, outperforming unscaffolded baselines and specialized provers.
- Ablation studies indicate that removing the tool-grounded architecture or separating the Planner and Builder each reduces performance by approximately 12 percentage points.
This framework enables reliable proof synthesis in underrepresented mathematical domains by leveraging explicit structural knowledge rather than relying solely on model capabilities.