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Related Articles from SNS
Formal Foundations and Proof-Carrying Certificates for q-ary Covering Codes in Lean 4
Announce Type: new Abstract: Covering codes in finite Hamming spaces ask for small sets of words whose Hamming balls cover the whole space. This paper presents a Lean 4 formalization of the elementary theory of q-ary covering codes, centered on certificate predicates for upper bounds, lower bounds, and exact covering numbers $K_q(n,r)$. The formalization proves the q-ary Hamming-ball volume formula, the sphere-covering lower bound, elementary exact cases, product and relation rules, and...
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,...
Lean 4 Machine-Verified Proof of P = NP via the Pedigree Polytope Membership Problem
arXiv:2606.03194v1 Announce Type: new Abstract: The Membership Problem for Pedigree Polytope (M3P) asks, given $X\in\mathbb{Q}^{\binom{n}{3}}$, whether $X\in\mathrm{conv}(P_n)$, where $P_n$ is the set of all pedigrees. A pedigree is a structured encoding of a Hamiltonian cycle construction in $K_n$. We establish that M3P is solvable in strongly polynomial time via a recursively constructed layered network $(N_k, R_k, \mu)$ and a multicommodity flow problem MCF$(k)$. The necessary and...
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.
Tridirectional Discriminating-Power Formal Verification of Smart Contract Reentrancy Defense Against Production-Deployed Solidity Source
Announce Type: replace Abstract: We present the first machine-checked correctness proof of the OpenZeppelin reentrancy-guard pattern against a Lean 4 state-machine model of production-deployed Solidity source. All thirteen theorems are machine-checked with zero sorry, zero user-introduced axioms, and an axiom footprint bounded by [propext] (a standard mathlib4 axiom), gated under continuous integration. Smart contract reentrancy has caused over US$500M in documented losses since 2016, with...
Tridirectional Discriminating-Power Formal Verification of Smart Contract Reentrancy Defense Against Production-Deployed Solidity Source
arXiv:2606.01794v1 Announce Type: new Abstract: We present the first machine-checked correctness proof of the OpenZeppelin reentrancy-guard pattern against a Lean 4 state-machine model of production-deployed Solidity source. All thirteen theorems are machine-checked with zero sorry, zero user-introduced axioms, and an axiom footprint bounded by [propext] (a standard mathlib4 axiom), gated under continuous integration. Smart contract reentrancy has caused over US$500M in documented losses...
Lean-GAP: A Dataset of Formalized Graduate Algebra Problems
arXiv:2606.02588v1 Announce Type: new Abstract: We present Lean-GAP (Lean-Graduate Agebra Problems), 430 formalized graduate-level algebra problems from the textbook Abstract Algebra by Dummit and Foote. We develop a scalable pipeline consisting of PDF-to-LaTeX preprocessing, autoformalization into Lean 4, and verification of informal-formal correspondence.
Evaluation of LLMs for Mathematical Formalization in Lean
arXiv:2606.05632v1 Announce Type: new Abstract: Within the past few years, the ability of Large Language Models (LLMs) to generate formal mathematical proofs has improved drastically. We provide a comparison of various LLMs' effectiveness in producing formal proofs in Lean 4 with the goal of assisting those seeking to use LLMs to support their own projects. We utilize both pass@$k$ and refine@$k$ metrics as the benchmark for our comparison and evaluate on subsets of both miniF2F and miniCTX...
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.
Automated Conjecture Resolution with Formal Verification
arXiv:2604.03789v2 Announce Type: replace Abstract: Recent advances in large language models have significantly improved their ability to perform mathematical reasoning, extending from elementary problem solving to increasingly capable performance on research-level problems. However, reliably solving and verifying such problems remains challenging due to the inherent ambiguity of natural language reasoning. In this paper, we propose an automated framework that integrates natural language...