AutoGraphForge Automates Graph Theory Discovery
💡See how AI combines graph search, counterexamples, and Lean verification to generate trustworthy mathematical conjecture
⚡ 30-Second TL;DR
What Changed
Uses counterexample-guided rounds in which Graffiti3 generates conjectures from a small, evolving graph-invariant table.
Why It Matters
AutoGraphForge demonstrates a scalable route toward AI-assisted mathematical discovery that combines empirical search with machine-checkable proofs. If the full pipeline proves reliable, it could help researchers explore large conjecture spaces while reducing the risk of accepting unsupported AI-generated claims.
What To Do Next
Prototype a small AutoGraphForge-style loop by combining graph-invariant generation, counterexample search, and Lean 4 kernel checking before trusting neural theorem-prover outputs.
Key Points
- •Uses counterexample-guided rounds in which Graffiti3 generates conjectures from a small, evolving graph-invariant table.
- •Tests candidates against roughly 348,000 graphs, including House of Graphs data, graph censuses, extremal families, and random models.
- •A novelty filter checks 559 classical and folklore relations using linear programming and symbolic substitutions.
- •The surviving conjectures are translated into Lean 4 statement skeletons and kernel-checked with pinned mathlib4.
- •Integrates DeepSeek-Prover-V2-671B and OProver-32B as neural proof candidates behind independent formal verification.
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Original source: ArXiv AI ↗
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