Final Report on the Mochizuki-Scholze-Stix Controversy

TL;DR

The paper confronts the Mochizuki–Scholze–Stix controversy over Inter-Universal Teichmüller Theory and the $abc$-conjecture. It introduces a $p$-adic Teichmüller framework and precisely defines Arithmetic Holomorphic Structures, arguing that many such deformations exist and can be organized into Arithmetic Teichmüller Spaces. It claims that Scholze–Stix's criticisms are unfounded and that a canonical theory aligning with Mochizuki's Principle of Inter-Universality is obtained, via the Joshi publications. The result is a Teichmüller-type perspective on arithmetic and a claimed proof of the $abc$-conjecture, with updated versions available on arXiv.

Abstract

This report provides my mathematical findings regarding the Mochizuki-Scholze-Stix controversy surrounding Mochizuki's Inter-Universal Teichmüller Theory.