Hypothesis-Disciplined Multi-Agent Automated Formalization of Asymptotic Statistical Theory
This work addresses the challenge of formalizing complex asymptotic statistical theory for the Lean 4 proof assistant, enabling verified mathematical reasoning in statistics.
The authors developed a multi-agent automated formalization pipeline for asymptotic statistical theory in Lean 4, achieving axiom-clean and source-faithful proofs of core parametric and semi-parametric theorems. The pipeline uses a hypothesis-disciplined audit to ensure every hypothesis is justified, resulting in a systematic formalization available on GitHub.
Asymptotic statistical theory is a challenging domain for AI-assisted formalization: its central results mix convergence statements, asymptotic expansions, functional analysis, and regularity conditions that have a large gap from existing infrastructure in Lean 4 formalization. To address these challenges, we propose a hypothesis-disciplined Lean 4 formalization pipeline built from multiple agents: a manager that coordinates seven specialist roles for proof planning, skeleton scaffolding, Mathlib reconnaissance, proof construction, integration, independent review, and audit. The main methodological discipline is the hypothesis-disciplined audit, implemented by the Auditor agent: every main-theorem hypothesis and concept-layer field must be anchored in the source mathematical prose, justified as a Lean encoding adapter, marked as source-implied, or rejected as an unsupported strengthening. Using this workflow, we build a systematic formalization of asymptotic statistical theory, especially the parametric and semi-parametric models' asymptotic distribution and efficiency results. The resulting Lean development is axiom-clean and source-faithful, with Lean-checked and human-audited proofs of core parametric and semi-parametric theorems organized so that theorem-agnostic infrastructure and statistical concept definitions are separated from theorem-specific assembly. The formalization results are available at https://github.com/junwei-lu/Lean-Asymptotic-Statistical-Theory.