 The main comparison in his theory remains unpublished as of 2019.Mochizuki's main comparison theorem in Hodge–Arakelov theory states (roughly) that the space of polynomial functions of degree less than "d" on the universal extension of a smooth elliptic curve in characteristic 0 is naturally isomorphic (via restriction) to the "d"2-dimensional space of functions on the "d"-torsion points.It is called a comparison theorem as it is an analogue for Arakelov theory of comparison theorems in cohomology relating de Rham cohomology to singular cohomology of complex varieties or étale cohomology of "p"-adic varieties.