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Lean

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3

RESEARCH · 1 SOURCE · arXiv cs.AI

Gemini-based agentic pipeline autonomously discovers and Lean-verifies new accelerations for 11 Busy Beaver (BB(6)) machines

arXiv:2610.22603v1 presents a Gemini-based agentic pipeline that combines pattern recognition, automated conjecturing, informal reasoning, and formal theorem proving in Lean to autonomously find compact, Collatz-like accelerations describing many execution steps of Turing machines. The system discovered and formally verified novel accelerations for eleven BB(6) machines, provisionally classifying them as "Cryptids"—machines with exact compact descriptions whose halting remains unresolved.

7.0

RESEARCH · 1 SOURCE · arXiv cs.AI

arXiv paper: verifier feedback can both help and harm self-repair in formal theorem proving

New arXiv paper (arXiv:2610.22698v1) studies verifier-guided self-repair in Lean theorem proving using frozen Qwen3.6-27B and DeepSeek-Prover-V2-7B on MiniF2F problems. It finds that conditioning a model on its failed proof often reduces success and increases copying of the failure, while showing the compiler error can recover performance for Qwen in some settings; overall, no tested feedback condition outperforms simple instruction-only resampling under matched token budgets.

6.0

RESEARCH · 1 SOURCE · arXiv cs.AI

arXiv paper: corrective feedback reduces discovery of specification counterexamples in Verus/Rust

The arXiv preprint (arXiv:2610.20676v1) shows that corrective correctness feedback can suppress discovery of programs that meet written contracts but violate intended behavior. On 12 Verus/Rust tasks across four model families under matched call budgets, independent no-feedback discovery more than doubles certified-witness yield versus IntentShield’s corrective-feedback loop (59.0% vs 27.1%); a phase-separated execution matches the aggregate yield without reusing responses, and preserving those witnesses yields stronger specification repair (Phase-Revised: 81.3% implementation success vs IS-Revised: 62.5%). The effect did not reproduce in available Dafny and Lean evaluations, suggesting an empirical boundary around the studied Verus/Rust workflow.

6.0