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1. Introduction
The purpose of this paper and its sequels [DH20b] and [DH20a] is to put Mochizuki's
inequality in a user friendly context for working mathematicians. While these manuscripts
do 1 indicate in some places how certain parts of Mochizuki's constructions work, they do not
attempt to give a proof of [Moc15c, Corollary 3.12]. Moreover we black-box and suppress
the anabelian geometry as much as possible (at some junctures this is simply not possible).
By the end of [DH20b] we will rigorously derive a variant of Theorem 1.10 of [Moc15d],
(an effective version of S