  This paper does not give a proof of Mochizuki's Corollary 3.12. It is the
first in a series of three papers concerning Mochizuki's Inequalities. The
present paper concerns the setup of Corollary 3.12 and the first two
indeterminacies, the second \cite{Dupuy2020c} concerns log-Kummer
correspondences and ind3, and the third \cite{Dupuy2020b} concerns applications
to Diophantine inequalities (in the style of IUT4). These manuscripts are
designed to provide enough definitions and background to give readers the
ability to apply Mochizuki's statements in their own investigations. Along the
way, we have faithfully simplified a number of definitions, given new auxillary
definitions, and phrased the material in a way to maximize the differences
between Theorem 1.10 of IUT4 and Corollary 3.12 of IUT3. It is our hope that
doing so will enable creative readers to derive interesting and perhaps
unforeseen consequences Mochizuki's inequality.
