My response to Mochizuki's Comments on my papers [Preprints: Construction of Arith. Holo. Strs I,II,II(1/2),III, IV]. I will restrict myself to mathematics.

My work shows that Mochizuki's [IUT 1-3] requires modern p-adic Hodge Theory and not group theory of the fundamental group as many may have previously believed. The theory of [IUT 1-3] is about working with distinct arithmetic holomorphic structures and averaging over the many distinct p-adic periods (of a fixed elliptic curve) they give rise to.

My work [Preprints: Constr. of Arith. Holo. Strs I,II,II(1/2),III] provides a precise way for doing this and provides the correct mathematical tools to discuss and verify Mochizuki's [IUT 4]. My [Preprint: Constr. of Arith. Holo. Strs IV] is Mochizuki's proof of the abc-conjecture, and I think that up to any necessary modifications of my preprints [Preprints: Constr. of Arith. Holo. Strs III, IV], we are now in a position to robustly verify the validity of the main theorem of [IUT 4]. My approach to [IUT4], based on my theory, is in [Preprint: Constr. of Arith. Holo. Strs IV].

It is my sincere hope that Mochizuki, who seems to be warming to my ideas, introduced in [Preprints: Constr. of Arith. Holo. Strs I,II,II(1/2),III], especially my use of perfectoids and untilts in this context, will help us arrive at the correct mathematical conclusions regarding [IUT 4], in spite of his current negativity about my papers themselves.

As my LaTeX source files of my preprints on arxiv.org will testify, I use the standard automated theorem numbering provided by AMSLaTeX (American Math. Society, LaTeX). Any numerical coincidences anyone finds in the theorem numbering in my papers must be considered entirely self-imagined.

My response to Mochizuki's Comments on my papers [Preprints: Construction of Arith. Holo. Strs I, II, II(1/2), III, IV. I will restrict myself to mathematics.

My work shows that Mochizuki's [IUT 1-3] requires modern p-adic Hodge Theory and not group theory of the fundamental group as many may have previously believed. The theory of [IUT 1-3] is about working with distinct arithmetic holomorphic structures and averaging over the many distinct p-adic periods (of a fixed elliptic curve) they give rise to.

My work [Preprints: Constr. of Arith. Holo. Strs I,II,II(1/2),III] provides a precise way for doing this and provides the correct mathematical tools to discuss and verify Mochizuki's [IUT 4]. My [Preprint: Constr. of Arith. Holo. Strs IV] is Mochizuki's proof of the abc-conjecture, and I think that up to any necessary modifications of my preprints [Preprints: Constr. of Arith. Holo. Strs III, IV], we are now in a position to robustly verify the validity of the main theorem of [IUT 4]. My approach to [IUT4], based on my theory, is in [Preprint: Constr. of Arith. Holo. Strs IV].

It is my sincere hope that Mochizuki, who seems to be warming to my ideas, introduced in [Preprints: Constr. of Arith. Holo. Strs I,II,II(1/2),III], especially my use of perfectoids and untilts in this context, will help us arrive at the correct mathematical conclusions regarding [IUT 4], in spite of his current negativity about my papers themselves.

As my LaTeX source files of my preprints on arxiv.org will testify, I use the standard automated theorem numbering provided by AMSLaTeX (American Math. Society, LaTeX). Any numerical coincidences anyone finds in the theorem numbering in my papers must be considered entirely self-imagined.