Hypothesis-Disciplined Multi-Agent Automated Formalization of Asymptotic Statistical Theory

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. Four contract-scoped agents construct, audit, prove, and repair this blueprint. These agents are coordinated by a two-stage orchestrator that first stabilizes target fidelity through adversarial review and then discharges the proof directed acyclic graph (DAG) from its dynamic leaves upward in parallel CI-gated rounds. LeanMarathon turns one brittle multi-hour run into many local, recoverable, parallel transactions. We evaluate LeanMarathon on two recent research papers spanning four Erdős problems (#1051, #1196, #164, #1217). Across three autonomous runs, it formalizes all seven target theorems with no sorry, proving 258 lemmas and theorems. These results show that reliable AI co-mathematics requires not only stronger provers, but durable harnesses that preserve target fidelity across long mathematical developments. The code can be found at https://github.com/YuanheZ/LeanMarathon.

While Large Language Models (LLMs) have demonstrated exceptional capabilities in mathematical reasoning, they frequently produce subtle errors that evade human detection. Formal mathematical languages like Lean 4 offer mechanical proof checking, strongly motivating the need for autoformalization: the automatic translation of natural language mathematics into verifiable code. Recent trends indicate that general-purpose LLMs, heavily optimized for standard programming, now outperform smaller models explicitly fine-tuned for Lean. Leveraging this shift, we introduce an agentic autoformalization framework powered by general coding LLMs. At the core of our system is an orchestrator that manages a multi-agent pipeline tailored for research-level mathematics. Because cutting-edge research frequently relies on concepts outside the scope of existing libraries like Mathlib, our system dynamically extends necessary type definitions and validates them via a novel Auxiliary Lemma technique before formalizing the primary theorems. We applied our approach to PutnamBench, producing machine-checked Lean proofs for a random sample of 32 problems. Furthermore, we evaluate our system on five papers from the ACM Symposium on Theory of Computing (STOC) spanning combinatorics, communication complexity, mechanism design, and learning theory, successfully formalizing their main theorems and validating the generated formalizations with human experts; for all five we also formalize the proofs alongside the statements, and notably two of them are proved with no axioms beyond Lean's kernel. All of our formalizations are available at https://beyondthelibrary.github.io/formal_arxiv .

AI-Scientist systems risk manufacturing spurious discoveries through uncontrolled multiple testing. We present a functional architecture that enforces statistical rigor at two levels: a Haskell embedded domain-specific language (the Research monad) that makes it impossible to test a hypothesis without updating the error budget, and a declarative scaffold, backed by an OS-level sandbox, that makes validation data physically absent from the environment in which LLM-generated code runs. We ground the design in a machine-checked Lean4 formalization of LORD++ online false-discovery-rate (FDR) control: we derive its error budget and prove both marginal and full FDR control, then close the gap to the implementation by verifying the budget's wealth invariant over IEEE754 arithmetic in SPARK/Ada. To our knowledge this is the first verified chain from theorem to floating-point implementation for an online FDR procedure. In simulation, the architecture holds the false discovery rate near 1% against a 5% target, where a naive approach reaches 41%. In end-to-end case studies, a valid test avoids the false discoveries a flawed one produces, yet still finds real effects when the data allow. An adversarial evaluation confirms that generated code cannot read the held-out data even when given its exact path.