\section*{Statement on the use of AI}
\addcontentsline{toc}{section}{Statement on the use of AI}
\markboth{Statement on the use of AI}{}

The mathematical arguments of the three papers of this series were
developed with GPT-6 Astra Pro. The papers were then organized and
rewritten with Claude Fable~5.2, and in the course of this several
arguments were replaced or expanded. The three papers were then
reviewed in detail, line by line, by GPT and Claude models, in
sessions which had not taken part in writing them, and the errors
found in this way were corrected.

Boyang Hu organized the work and is responsible for the manuscript.