A remark on the AI proof of the Deligne--Drinfeld conjecture

Abstract

We give a geometric interpretation of the projection and reconstruction underlying the Open AI's characteristic-two proof of the Deligne--Drinfeld conjecture. Using the double covering and filling a puncture, we construct a morphism on normalized level-two associators with an explicit inverse on its image. We compute the restricted tangent reconstruction in the pro-2 realization and identify the leading coefficient maps with those of the OpenAI proof, making its implicit reconstruction explicit.