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基礎論くんか ；ｐ）

>IUTをサポートする研究がでてこない。

あるよ
下記のベンジャミン・コラスの寄稿があるよ
よく書けていると思う

https://ja.wikipedia.org/wiki/%E5%AE%87%E5%AE%99%E9%9A%9B%E3%82%BF%E3%82%A4%E3%83%92%E3%83%9F%E3%83%A5%E3%83%A9%E3%83%BC%E7%90%86%E8%AB%96
宇宙際タイヒミュラー理論
2023年1月、RIMSのベンジャミン・コラスはMathematics and Theoretical Computer Science誌にレビューを寄稿した[29]。[28]
28^“ANABELIAN ARITHMETIC GEOMETRY - A NEW GEOMETRY OF FORMS AND NUMBERS: Inter-universal Teichmüller theory or “beyond Grothendieck’s vision” Benjamin Collas Version 11/15/2023”.
https://collas.perso.math.cnrs.fr/documents/Collas-Anabelian%20Arithmetic%20Geometry-IUT.pdf
(抜粋)
A PANORAMA OF GROTHENDIECK’S ANABELIAN PHILOSOPHY At the most elementary level of human cognition, the essence of anabelian arithmetic geometry concerns the articulation– and possible reconciliation– of two a priori complementary ways of deciphering the perceptible world, that is to say, the discrete and continuous realms. The discreteness of number theory– or its geometric variation, Diophantine geometry– imposes constraints on the transcendental nature of the mind, while the continuous nature of geometry– or its discrete variation, arithmetic geometry– furnishes a comfortable receptacle for its various realizations.

§ Grothendieck’s Mathematics Philosophy.
In response to the limitations of the human mind to grasp the essence of the dichotomy between the discrete and the continuous, Grothendieck’s approach is to propose a universal and structural vision that reconciles the two realms (the discrete and the continuous)– each as an avatar of a unique functorial and category-theoretic construction, see Fig. 1 below and [R&S] more generally. This approach is both philosophical and practical: languages are constructed that reveal pre-existing structures, which, in turn, stimulate the further development of language1. In Grothendieck’s twelve themes legacy, the unified treatment of Galois symmetries of numbers and geometric forms– i.e., anabelian geometry and Galois-Teichmüller theory– is presented as a “master theme” to the mathematical community, see Fig. 2 and ibid.

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