arXiv:2604.03789v1 Announce Type: cross 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 for tackling research-level mathematical problems that integrates natural language reasoning with formal verification, enabling end-to-end problem solving with minimal human intervention. Our framework consists of two components: an informal reasoning agent, Rethlas, and a formal verification agent, Archon. Rethlas mimics the workflow of human mathematicians by combining reasoning primitives with our theorem search engine, Matlas, to explore solution strategies and construct candidate proofs. Archon, equipped with our formal theorem search engine LeanSearch, translates informal arguments into formalized Lean 4 projects through structured task decomposition, iterative refinement, and automated proof synthesis, ensuring machine-checkable correctness. Using this framework, we automatically resolve an open problem in commutative algebra and formally verify the resulting proof in Lean 4 with essentially no human involvement. Our experiments demonstrate that strong theorem retrieval tools enable the discovery and application of cross-domain mathematical techniques, while the formal agent is capable of autonomously filling nontrivial gaps in informal arguments. More broadly, our work illustrates a promising paradigm for mathematical research in which informal and formal reasoning systems, equipped with theorem retrieval tools, operate in tandem to produce verifiable results, substantially reduce human effort, and offer a concrete instantiation of human-AI collaborative mathematical research.

arXiv:2603.16790v3 Announce Type: replace-cross Abstract: Recent code large language models have achieved remarkable progress on general programming tasks. Nevertheless, their performance degrades significantly in industrial scenarios that require reasoning about hardware semantics, specialized language constructs, and strict resource constraints. To address these challenges, we introduce InCoder-32B (Industrial-Coder-32B), the first 32B-parameter code foundation model unifying code intelligence across chip design, GPU kernel optimization, embedded systems, compiler optimization, and 3D modeling. By adopting an efficient architecture, we train InCoder-32B from scratch with general code pre-training, curated industrial code annealing, mid-training that progressively extends context from 8K to 128K tokens with synthetic industrial reasoning data, and post-training with execution-grounded verification. We conduct extensive evaluation on 14 mainstream general code benchmarks and 9 industrial benchmarks spanning 4 specialized domains. Results show InCoder-32B achieves highly competitive performance on general tasks while establishing strong open-source baselines across industrial domains.