Unified Geometric Predictions for Universal Physical Boundaries: Analytical Correlation between Euler's Number, the Golden Ratio, and the Space-Time Constant 1.26

Abstract: A New Geometric Paradigm of the Cosmic Metabolic System This paper presents a novel geometric paradigm where the physical boundaries of the universe are defined by fundamental mathematical constants. Minimum Scale: Predicted to be dependent on Euler's number (e). Maximum Scale: Defined by the Golden Ratio (\phi). The Bridge: The constant 1.26 (\sqrt[3]{4}) is identified as a density gradient that resolves the Pioneer anomaly. This unified approach demonstrates that the universe functions as a self-sustaining metabolic system. [Conceptual Definition of the Term "Mina" and Clarification]1. Spiritual and Philosophical Origin:The previous terminology, "Amateras," was chosen not as a physical label, but as a symbolic representation of a "Messianic Light" (similar to the concept of Christ)—a fundamental energy that brings order and salvation to the chaotic structure of the universe. In our refined theory, this essence is fully inherited by the term "Mina". It represents the "All-Encompassing Source" that guides the circulation of the cosmos.2. Absolute Distinction from the "Amateras Particle":I must state with absolute clarity: This theory has NO relation, physical or otherwise, to the ultra-high-energy cosmic ray known as the "Amateras particle" detected in 2021.The naming was purely a philosophical choice and was not intended to reference existing astrophysical data. To prevent further scientific confusion, we have transitioned all terminology to "Mina-particle" to emphasize its unique identity as the core of the Mina-Taisuke Circulation Theory.