@Madeleine Birchfield

My recently released paper (Constructions III) proves many versions of Corollary 3.12 including Mochizuki’s version and I provide a `Rosetta Stone’ which facilitates a detailed comparison of the two theories. My formulation and proof of the geometric case of Corollary 3.12 is given in Constructions II(1/2). 

The abc-conjecture is an expected, but delicate consequence of Corollary 3.12 (and some other results) and my conclusions (with proofs) will appear in my forthcoming paper: Construction of Arithmetic Teichmuller Spaces IV. 

To clarify the discussion about upper bounds, let me say that Mochizuki does not deal with upper bounds on this set in IUT III but takes this up in IUT IV. In my case too, upper bounds are taken up in my forthcoming paper, Constructions IV.