>>50 補足
>Ans. True. Let me discuss this now. Here is what Mochizuki says ([Mochizuki, 2021b, Page 26]):

ここをもう少し関連部分と共に引用しよう
それが、下記ですが ”basepoint”が重要キーワードで
basepointに関連して”the distinct set-theoretic ”があると考えているらしい
そのuniversesをつなぐので ”that we refer to as inter-universal”だと

しかし この用語は >>13 薄葉 季路 (早大理工) 集合論の宇宙 —Universe と Multiverse—
における 基礎論用語”集合論の宇宙”とは 全く異なりますね

(参考)
https://www.kurims.kyoto-u.ac.jp/~motizuki/papers-japanese.html
望月 論文サイト
[1] Inter-universal Teichmuller Theory I: Construction of Hodge Theaters. PDF NEW !! (2020-05-18)
https://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20I.pdf
P21
§I3. Basepoints and Inter-universality
In particular, the only data that can be considered in relating ´etale fundamental groups on either side of a filter is the ´etale-like structure constituted by the underlying abstract topological group associated to such an ´etale fundamental group, i.e., devoid of any auxiliary data arising from the construction of the group “as an ´etale fundamental group associated to a basepoint determined by a geometric point of a scheme”. It is this fundamental aspect of the theory of the present series of papers — i.e.,
of relating the distinct set-theoretic universes associated to the distinct fiber functors/basepoints on either side of such a non-ring/scheme-theoretic filter
—that we refer to as inter-universal.
This inter-universal aspect of the theory manifestly leads to the issue of considering
the extent to which one can understand various ring/scheme structures by considering only the underlying abstract topological group of some ´etale fundamental group arising from such a ring/scheme structure
—i.e., in other words, of considering the absolute anabelian geometry [cf. the Introductions to [AbsTopI], [AbsTopII], [AbsTopIII]] of the rings/schemes under consideration.