  This paper deals with consequences of the existence of Arithmetic Teichmuller
spaces established in https://arxiv.org/abs/2106.11452 and
https://arxiv.org/abs/2210.11635. Theorem~9.2.1 provides a proof of a local
version of Mochizuki's Corollary~3.12. Local means for a fixed $p$-adic field.
There are several new innovations in this paper. Some of the main results are
as follows. Theorem~3.5.1 shows that one can view the Tate parameter of Tate
elliptic curve as a function on the arithmetic Teichmuller space of [Joshi,
2021a], [Joshi, 2022b]. The next important point is the construction of
Mochizuki's $\Theta_{gau}$-links and the set of such links, called Mochizuki's
Ansatz in {\S}6. Theorem~6.9.1 establishes valuation scaling property satisfied
by points of Mochizuki's Ansatz (i.e. by my version of $\Theta_{gau}$-links).
These results lead to the construction of a theta-values set ({\S}8) which is
similar to Mochizuki's Theta-values set (differences between the two are in
{\S}8.7.1). Finally Theorem~9.2.1 is established. For completeness, I provide
an intrinsic proof of the existence of Mochizuki's $\log$-links (Theorem
10.9.1), $\mathfrak{log}$-links (Theorem~10.15.1) and Mochizuki's log-Kummer
Indeterminacy (Theorem~10.20.1) in my theory.
