The UMA Monad Theory: A Number-Theoretic Philosophy of Division by Zero | ウマモナド理論: ゼロ除算に関する数論哲学

This thesis aims to redefine the very existence of emptiness and infinity by reimagining the origin of numbers in addition and multiplication—not as static symbols such as "0" or "1," but as a multi-layered cosmic model in which the law of conservation of energy functions dynamically, while also exploring the possibility of division by zero. This work serves as a sketch of number-theoretic philosophy, acting as a preliminary stage to rigorous mathematical proof. In this model, following Leibniz, the "Monad" is established as the smallest unit of existence. By reinterpreting "0" not as a mere singularity but as an "exit" for dimensions, this paper discusses the necessity of an absolute zero point---the "Universal Mapping Absolute (UMA) Monad"---which integrates addition and multiplication without contradiction. (This has the potential to provide fundamental meaning to the limits of physics and the origins of noncommutative geometry.) 本論は、加法と乗法における数の起源を「0」や「1」という静的な記号としてではなく、エネルギー保存則が動的に機能する多層的な宇宙モデルとして捉え直すことで、空と無限の存在自体の再定義を予想し、ゼロ除算の可能性を考える。数理的な厳密な証明の前段階としての、数論哲学スケッチである。 本モデルでは、ライプニッツに倣い「モナド(Monad)」を存在の最小単位と設定する。ここでは「0」を特異点と見なさず、次元の「出口」として再解釈することで、加法と乗法を矛盾なく統合する絶対的零点「Universal Mapping Absolute(UMA)モナド」の必要性を論じる。(これは、物理学の限界点や非可換幾何学の原点に根本的な意味を与える可能性がある。)