Construction of Arithmetic Teichmuller Spaces III: A 'Rosetta Stone' and a proof of Mochizuki's Corollary 3.12
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also completely unnecessary, since distinct arithmetic holomorphic structures *do* exist for canonical reasons [Joshi, 2021a, 2022]. Notably, [Mochizuki, 2022] suggests the existence of distinct arithmetic holomorphic structures but it is not clearly established in [Mochizuki, 2021a,b,c]
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arithmetic holomorphic structures are central to [Mochizuki, 2021a,b,c,d] and the present series of papers ([Joshi, 2021a, 2022, 2023b,a] and this paper) is the only one which treats arithmetic holomorphic structures in detail and establishes their existence in the context of [Mochizuki, 2021a,b,c,d].
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Notably, [Mochizuki, 2022] suggests the existence of distinct arithmetic holomorphic structures but it is not clearly established in [Mochizuki, 2021a,b,c], nor can it be quantitatively established using the framework of [Mochizuki, 2021a,b,c] or [Mochizuki, 2012, 2013, 2015].
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