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南出論文
”The astronomically large constants in the inequalities established in Theorem 5.3 reflect the explicit [i.e., “non-conjectural”] nature of inter-universal Teichm¨uller theory. ”
いやいやいや
確かに、”The astronomically large constants”ですね
まだ改善の可能性ありという気がします

http://www.kurims.kyoto-u.ac.jp/~motizuki/Explicit%20estimates%20in%20IUTeich.pdf
Explicit Estimates in Inter-universal Teichmuller Theory. PDF NEW!! (2020-11-30) いわゆる南出論文

P44
Remark 5.3.1.
The astronomically large constants in the inequalities established in Theorem 5.3 reflect the explicit [i.e., “non-conjectural”] nature of inter-universal Teichm¨uller theory.
Their size may seem quite unexpected,
especially from the point of view of the classical [“conjectural”] literature on
such inequalities, where sometimes it is even naively assumed that these
constant may be taken to be as small as 1.