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This paper deals with consequences of the existence of Arithmetic Teichmullerspaces established in https://arxiv.org/abs/2106.11452 andhttps://arxiv.org/abs/2210.11635. Theorem~9.2.1 provides a proof of a localversion 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 areas follows. Theorem~3.5.1 shows that one can view the Tate parameter of Tateelliptic curve as a function on the arithmetic Teichmuller space of [Joshi,2021a], [Joshi, 2022b]. The next important point is the construction ofMochizuki's $\Theta_{gau}$-links and the set of such links, called Mochizuki'sAnsatz in {\S}6. Theorem~6.9.1 establishes valuation scaling property satisfiedby 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 issimilar 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 providean intrinsic proof of the existence of Mochizuki's $\log$-links (Theorem10.9.1), $\mathfrak{log}$-links (Theorem~10.15.1) and Mochizuki's log-KummerIndeterminacy (Theorem~10.20.1) in my theory.

Construction of Arithmetic Teichmuller spaces II: Proof of a local prototype of Mochizuki's Corollary 3.12