Computational analysis reveals the exact numerical impact of separating structural steps in local field estimates, highlighting the sensitivity of bounds in inter-universal Teichmüller theory.
A third report in the series begun by 10.5281/zenodo.22537342 and continued in 10.5281/zenodo.22601333. The local estimates of Mochizuki, Inter-universal Teichmüller Theory IV, §1, are assembled from several steps that the source keeps apart: a p-primary torsion term, a normalization dividing by the local degree, a tensor order sitting inside its own normalization, a floor function, a ramification support, and a weighting of places. This report computes, in actual local fields and for named curves, what each of those separations is worth: how far the estimate moves if one of them is elided and nothing else is changed. The answers are exact rationals or exact multiples of log p. Nothing here is offered as a correction to the source, and no claim is made about [IUT III, Corollary 3.12], about the objections of Scholze–Stix, or about the abc conjecture. Formulas printed in the source are marked [S] and exact computations from them [P]; two places where the distinction being measured is the author's own rather than the source's are marked as such in the text. The artifact contains a standard-library Python script computing twelve tables, each asserting its own conclusion; a frozen presentation contract that fails if any printed row changes; and a regression gate of thirty-one named single-token defects, all of which the shipped script rejects. Four independent external reviews of earlier drafts are reflected in this version.
No takes yet. Share an insight, caveat, or question.
Toshihisa Urahigashi (2026) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: