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

• URL: http://arxiv.org/abs/2606.20642v1
• Date: Wed, 03 Jun 2026 20:03:38 GMT
• Title: Hypothesis-Disciplined Multi-Agent Automated Formalization of Asymptotic Statistical Theory
• Abstract summary: Asymptotic statistical theory is a challenging domain for AI-assisted formalization.<n>We propose a hypothesis-disciplined Lean 4 formalization pipeline built from multiple agents.<n>The resulting Lean development is axiom-clean and source-faithful.
• Score: 17.20738506776148
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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