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Mochizuki has this 1 page pdf posted on his website that tries to explain Inter-universal Teichmuller Theory through analogy to a Japanese animation: http://www.kurims.kyoto-u.ac.jp/~motizuki/sokkuri-hausu-link...

I wish I could find the animation itself, but that link is broken.

Song from the album: http://youtu.be/feOLbipVGEU

If you find a copy of his explanation in Japanese I'll try to see if he's referring to a literal animation or not. I couldn't find one and he doesn't really refer to anything beyond the theme/concept and the girl's theta-like eyes.

Edit: Something else I found (https://www.jstage.jst.go.jp/article/essfr/6/3/6_160/_pdf).

Is that article written by Mochizuki? Can you make sense of it?

It is not written by Mochizuki (望月新一), but rather by Shiraki Yoshinao (白木善尚). You can see his profile here: http://www.sci.toho-u.ac.jp/is/lab/shiraki_lab/shiraki.html

I didn't really get much from it even with some assistance, but the very first part is a quick dialogue about a universe king and a neighbor universe king exchanging New Years gifts. Section 7 is about the そっくりハウス and goes with the page you linked, but ends by saying something about the multiplicative and additive rotational properties have something to do with the different universes seeing each other. He compares the girl's excitement to Mochizuki's upon discovering the identical house inside of a house.

Someone with better command could give a much better summary, but I'd personally be more interested in the lecture Mochizuki gave himself on it IUTeich last week (according to his site).

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