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Optimizing the Cost-Quality Tradeoff of Agentic Theorem Provers in Lean

arXiv:2606.04883v1 Announce Type: new Abstract: Large language models (LLMs) are increasingly used in workflows for generating formal proofs in Lean. These workflows often decompose problems into smaller lemmas, sample many proof attempts, and use compiler feedback to guide search. However, they can be prohibitively expensive, often spending substantial compute on attempts that ultimately fail.

arXiv CS 6d ago

A formal proof of the Ramanujan--Nagell theorem in Lean 4

arXiv:2604.09808v2 Announce Type: replace-cross Abstract: We present a complete formalization, in the Lean interactive theorem prover with the Mathlib library, of the Ramanujan--Nagell theorem: the only integer solutions to the Diophantine equation $x^2 + 7 = 2^n$ are $(n,x) \in \{(3,\pm1),(4,\pm3),(5,\pm5),(7,\pm11),(15,\pm181)\}$. The formalization includes all dependencies, notably the computation of the ring of integers of the quadratic field $\mathbb{Q}(\sqrt{-7})$, its class number,...

arXiv CS 8d ago

Progress in Formalizing Sphere Packing in Dimension 8

arXiv:2604.23468v3 Announce Type: replace-cross Abstract: In 2016, Viazovska famously solved the sphere packing problem in dimension $8$, using modular forms to construct a 'magic' function satisfying optimality conditions determined by Cohn and Elkies in 2003. In March 2024, Hariharan and Viazovska launched a project to formalize this solution and related mathematical facts in the Lean Theorem Prover. A significant milestone was achieved in February 2026: the result was formally verified,...

arXiv CS 9d ago

Expected Value Alignment for Generative Reward Modeling in Formal Mathematics Verification

new Abstract: Large Language Models (LLMs) are increasingly used with formal interactive theorem provers such as Lean 4. Scaling these systems with reinforcement learning or search methods requires process reward models (PRMs) that can evaluate intermediate reasoning steps. Existing reward-model designs expose a practical trade-off.

arXiv CS 8d ago

ProofWala: A Framework for Multilingual Proof Data Synthesis and Theorem-Proving

arXiv:2502.04671v3 Announce Type: replace Abstract: Neural approaches to theorem proving require robust infrastructure for interfacing with interactive theorem provers (ITPs), extracting structured proof data, and executing proof search at scale. However, existing tooling is often assistant-specific and oriented toward file-level execution, making repository-scale analysis and parallel experimentation challenging. We present ProofWala, a multilingual proof engineering framework built around...

arXiv CS 9d ago

Goedel-Architect: Streamlining Formal Theorem Proving with Blueprint Generation and Refinement

Announce Type: new Abstract: We introduce Goedel-Architect, an agentic framework for formal theorem proving in Lean 4 centered on blueprint generation and refinement. A blueprint is a dependency graph of definitions and lemmas that builds up to the main theorem. First, Goedel-Architect generates a blueprint of formally stated definitions and lemmas, along with declared dependencies.

arXiv CS 5d ago

Formally Solving Answer-Construction Problems in Lean

arXiv:2505.18492v5 Announce Type: replace Abstract: Mathematical competition problems fall into two broad types: theorem proving, which asks for a proof of a given statement, and answer construction, which requires constructing a property-satifying object with proofs. With recent advances in large language models (LLMs), formal theorem-proving techniques have made substantial progress on theorem-proving problems, yet formal answer construction remains less studied. This exposes a mismatch...

arXiv CS 8d ago

LeanMarathon: Toward Reliable AI Co-Mathematicians through Long-Horizon Lean Autoformalization

Announce Type: new Abstract: Long-horizon autoformalization of research mathematics fails not only at hard lemmas, but at scale: statements drift, dependencies tangle, context decays, and local repairs corrupt distant work. We present LeanMarathon, a multi-agent harness for reliable research-level Lean autoformalization. Its core abstraction is an evolving blueprint: a Lean file that serves simultaneously as formal proof skeleton, natural-language proof graph, and shared system of record.

arXiv CS 5d ago