An Integral-Structure Inflation in the Hull Operation of IUT Corollary 3.12
This paper identifies and rigorously quantifies a third-class gap in the passage from Theorem 3.11 to Corollary 3.12 in S. Mochizuki's inter-universal Teichmuller theory (IUT). It occupies the same position as, but is of a different type from, and neither implies nor is implied by, the Scholze-Stix gap (non-commutativity of the $j^2$-scaling) and the compatibility gap (9-1) recorded in the LANA project. The holomorphic hull of IUT III, Remark 3.9.5, is the minimum over the constrained family $\{\lambda \cdot \mathcal{O}\}$: each direct summand of $I^{\mathbb{Q}} \cong \bigoplus_{\alpha}…
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