| _version_ | 1866901757582376960 |
|---|---|
| author | Ueoka, Yoshiki |
| author_facet | Ueoka, Yoshiki |
| contents | <p>This paper organizes the foundational framework of the Meikyo–Shisui Theory, proposed<br>by the author, and presents a proposal for a translation theory that enables mutually rein-<br>terpreting mathematical objects within a unified formal structure. Although this framework<br>does not necessarily aim at directly providing solutions, a central feature is that the process<br>of translation itself gives rise to new perspectives and generates new questions. Depending<br>on the situation, the translation process may also crystallize directly into a solution, in the<br>form of a procedure or a proof strategy.<br>The theory is constructed using a small number of technical terms: the choice of ob-<br>jects (Sui), the rules associated with them (Getsu), their interface (Sui–Getsu), the up-<br>date rule called the Natural Move (NM), and the extracted essence (Shin-Getsu). Here,<br>Sui/Getsu/Shin-Getsu are not literal translations but are used as proper technical terms,<br>and the term “move” in Natural Move is used in the sense of an update or transition step.<br>To facilitate understanding, this paper presents, not representative examples but minimal<br>sketches: a Collatz-type iteration as an example of a dynamic problem, and a Goldbach-type<br>proposition as an example of a static problem. Through three approaches—retrospective<br>tracing, emergence, and phase transition—we clarify what should be identified, such as the<br>identification of Sui or Getsu, or the definition of the Natural Move. This framework naturally<br>extends to iterative systems, search and optimization, rewriting systems, finite verification,<br>and graph operations, and provides a viewpoint in which the problem itself emerges through<br>the process of translation.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18579966 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Foundations of the Meikyo–Shisui Theory Ueoka, Yoshiki 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 <p>This paper organizes the foundational framework of the Meikyo–Shisui Theory, proposed<br>by the author, and presents a proposal for a translation theory that enables mutually rein-<br>terpreting mathematical objects within a unified formal structure. Although this framework<br>does not necessarily aim at directly providing solutions, a central feature is that the process<br>of translation itself gives rise to new perspectives and generates new questions. Depending<br>on the situation, the translation process may also crystallize directly into a solution, in the<br>form of a procedure or a proof strategy.<br>The theory is constructed using a small number of technical terms: the choice of ob-<br>jects (Sui), the rules associated with them (Getsu), their interface (Sui–Getsu), the up-<br>date rule called the Natural Move (NM), and the extracted essence (Shin-Getsu). Here,<br>Sui/Getsu/Shin-Getsu are not literal translations but are used as proper technical terms,<br>and the term “move” in Natural Move is used in the sense of an update or transition step.<br>To facilitate understanding, this paper presents, not representative examples but minimal<br>sketches: a Collatz-type iteration as an example of a dynamic problem, and a Goldbach-type<br>proposition as an example of a static problem. Through three approaches—retrospective<br>tracing, emergence, and phase transition—we clarify what should be identified, such as the<br>identification of Sui or Getsu, or the definition of the Natural Move. This framework naturally<br>extends to iterative systems, search and optimization, rewriting systems, finite verification,<br>and graph operations, and provides a viewpoint in which the problem itself emerges through<br>the process of translation.</p> |
| title | Foundations of the Meikyo–Shisui Theory |
| topic | 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 |
| url | https://doi.org/10.5281/zenodo.18579966 |