タイトル:無限潜在性の理論:ゼータ関数の非自明な零点における$1/f$順序と$1/2$軸の幾何学的必然性―不確実性と自由意志の出現に関する研究 Abstract: This paper proposes a novel, non-perturbative cosmological framework that conceptualizes the origin of the universe and fundamental physical constants through the lens of dynamic, geometric synchronization. This framework define the primordial trigger of the Big Bang at the Planck epoch ($10^{-43}$ s) as a trans-synchronization process restricted to the fundamental mathematical constants $\{i, \pi\}$ and the golden ratio $\Phi$, intentionally omitting Euler’s number $e$ to represent the undifferentiated state prior to exponential thermodynamic growth. Furthermore, we provide a structural, macro-equivalent interpretation of the Yang-Mills mass gap by mapping the confinement dynamics onto a stabilized linear relation ($y = ax + b$). In this model, the confinement energy ($ax$) and the non-zero mass intercept ($b$) are topologically secured via a geometric "phase lock" onto the $1/2$ critical line of the Riemann zeta function. By constraining the physical manifold strictly to three-dimensional space (Reality3D) to ensure global geometric consistency, this theory demonstrates that the deterministic order and stable mass-generation of the cosmos emerge as an inevitability of geometric necessity, preventing chaotic collapse into infinite potential.