WP_023 Mesoamerican and Pre-Columbian Cosmologies: Cyclic Temporal Geometries, Topological Closures, and Non-Linear Spacetime Manifolds / 中美洲與前哥倫布文明宇宙觀:週期時間幾何、拓撲閉合與非線性時空流形

This paper serves as Working Paper No. WP_023 in the Global Ontological Isomorphism Network series. It reconstructs the temporal metaphysics of Pre-Columbian Mesoamerican civilizations—specifically Mayan calendrics (*Tzolkin* / *Haab*) and Aztec cyclical cosmologies (*Sun Ages*)—by mapping their non-linear, periodic universe onto modern differential topology, **Closed Timelike Curves (CTCs)**, and **topological closures** on compact manifolds ($S^1 \times \mathcal{M}^3$). By applying general relativity, cosmic phase transition dynamics, and quantum measurement theory, this study demonstrates that:1. Mesoamerican cosmologies do not treat time as a linear arrow or an empty Newtonian parameter, but as a multi-dimensional spatialized geometric entity (*Kin*) with intrinsic curvature, energy-momentum density, and periodic boundary conditions.2. The 52-year Calendar Round generated by the topological interlocking of the *Tzolkin* and *Haab* wheels corresponds mathematically to a compactified temporal dimension ($S^1$) and closed phase trajectories ($\oint_{\mathcal{C}} ds^2 = 0$).3. The doctrine of the Five Sun Ages is isomorphic to vacuum state decays ($V(\phi_{\text{old}}) \to V(\phi_{\text{new}})$) and inflationary epochal phase transitions in non-equilibrium cosmic field theory.4. Mesoamerican ritual practices (such as the Aztec *Xiuhmolpilli* / New Fire Ceremony) are formalized as precision active phase control operations ($\hat{\mathcal{P}}_{\text{Xiuhmolpilli}}$) and metric regularizations that quench phase fluctuations ($\delta g_{\mu\nu} \to 0$) during critical topological phase transitions. This work integrates directly into Module II (Holographic Geometry & Spacetime Emergence) of the higher-education curriculum architecture for world philosophy and quantum metaphysics. --- 本文為「全球本體論同構網絡」系列之 Working Paper No. WP_023。本研究透過將瑪雅曆法(*Tzolkin* / *Haab*)與阿茲特克宇宙論(太陽紀)之非線性週期宇宙映射至微分拓撲、**封閉類時曲線(CTCs)** 與緊緻流形($S^1 \times \mathcal{M}^3$)上的**拓撲閉合(Topological Closure)**,重構了前哥倫布時期美洲文明的時間形上學。 透過應用廣義相對論、宇宙相變動態學與量子測量理論,本研究證成:1. 中美洲宇宙觀並未將時間視為單向箭頭或被動的牛頓參數,而是視為具備內在曲率、能量-動量密度與週期邊界條件的多維空間化幾何實體(*Kin*)。2. 由卓爾金曆與哈布曆太陽輪拓撲相扣產生的 52 年曆法紀元,在數學上對應於緊緻化時間維度($S^1$)與閉合相位軌跡($\oint_{\mathcal{C}} ds^2 = 0$)。3. 五大太陽紀學說同構於非平衡態宇宙場論中的真空態衰變($V(\phi_{\text{old}}) \to V(\phi_{\text{new}})$)與膨脹紀元相變。4. 前哥倫布文明的儀式實踐(如阿茲特克 *Xiuhmolpilli* / 新火儀式)被形式化為精準的主動相位調控操作($\hat{\mathcal{P}}_{\text{Xiuhmolpilli}}$)與度規正則化,能在關鍵拓撲相變期間淬滅位相波動($\delta g_{\mu\nu} \to 0$)。 本論文直接整合併納入高等教育「世界哲學史與量子形上學」之模組二(全息幾何與時空拓撲湧現)教學架構中。