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Bibliographic Details
Main Author:	Ueoka, Yoshiki
Format:	Recurso digital
Language:	English
Published:	Zenodo 2026
Subjects:	Meikyo > Shisui Theory translation framework mathematical translation problem structure representation state space update rule Natural Move equivalence classes absorbing sets dynamical systems Collatz conjecture Goldbach conjecture rewriting systems finite verification
Online Access:	https://doi.org/10.5281/zenodo.18579966
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Table of Contents:

This paper organizes the foundational framework of the Meikyo–Shisui Theory, proposed by the author, and presents a proposal for a translation theory that enables mutually rein- terpreting mathematical objects within a unified formal structure. Although this framework does not necessarily aim at directly providing solutions, a central feature is that the process of translation itself gives rise to new perspectives and generates new questions. Depending on the situation, the translation process may also crystallize directly into a solution, in the form of a procedure or a proof strategy. The theory is constructed using a small number of technical terms: the choice of ob- jects (Sui), the rules associated with them (Getsu), their interface (Sui–Getsu), the up- date rule called the Natural Move (NM), and the extracted essence (Shin-Getsu). Here, Sui/Getsu/Shin-Getsu are not literal translations but are used as proper technical terms, and the term “move” in Natural Move is used in the sense of an update or transition step. To facilitate understanding, this paper presents, not representative examples but minimal sketches: a Collatz-type iteration as an example of a dynamic problem, and a Goldbach-type proposition as an example of a static problem. Through three approaches—retrospective tracing, emergence, and phase transition—we clarify what should be identified, such as the identification of Sui or Getsu, or the definition of the Natural Move. This framework naturally extends to iterative systems, search and optimization, rewriting systems, finite verification, and graph operations, and provides a viewpoint in which the problem itself emerges through the process of translation.

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