  There was a lot of controversy about corollary 3.12, which was described in
the paper Inter-universal Teichmuller Theory III. In this article, another
proof of Corollary 3.12 will be derived, where the basis of the proof will be
the Erdos-Kac theorem. Also in Inter-universal Teichmuller Theory IV it was
said that the theory has a strong connection with the theory of Weil
cohomology, based on this connection, very important physical applications will
be derived in this article: generalization of non-Abelian Hodge correspondence,
non-Abelian gauge theory, proof of the mass gap based on corollary 3.12, T
duality is $\Theta^{\pm ell}$NF Hodge Theater, the limit at which a black hole
appears, the inflationary growth of the universe for the observer.
