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This work aims to analyze the attempted repair of a quantitative gap in Mochizuki's IUTchIII related to the abc conjecture.

June 15, 2026Open Access

The Gap in IUTchIII, Corollary 3.12: From Attempted Repair to Structural Diagnosis

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Reported repairs of the quantitative gap in IUTchIII's Corollary 3.12, indicating unresolved structural issues.

This work aims to analyze the attempted repair of a quantitative gap in Mochizuki's IUTchIII related to the abc conjecture.
Proved that the j-averaged archimedean residual A^tors < 0 and all non-archimedean residuals are negative.
Assessed contributions from IUT theta values and direct Tate-curve theta/eta/Jacobi torsion products.
Implemented a structural-diagnosis ledger for clearer presentation of claims and boundaries.
Confirmed that positive non-archimedean contributions grow as O(l^2), unable to be compensated by standard O(l) methods.
Verified independence of the R_base^tors < 0 finding regarding the j-averaged archimedean structure.
Maintained synchronization between English and German versions of the manuscript, ensuring accessibility.

Lukas Geiger (2026) studied this question.

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