The Statement of Mochizuki's Corollary 3.12, Initial Theta Data, and the First Two Indeterminacies

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.