An AI-Assisted Formalization of the Poincar\'e Conjecture

The paper reports an AI-assisted Lean 4 formalization of the Poincaré conjecture, beginning with limited reusable formal infrastructure for the geometric analysis. The authors combined a mathematician-prepared proof blueprint with explicit milestone statements, enabling parallel agent work and clear points for identifying blockers and providing guidance. Their analysis highlights the human interventions and organizational choices that shaped this workflow, and suggests that developing reusable infrastructure could reduce the cost of verifying future mathematical results in geometric analysis.

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