From Cantor Space to Calabi–Yau Manifolds: A Forward Derivation in Discrete Geometry

Integrated Abstract Summarises the core connections among the four parts, rather than a simple concatenation. For example: Starting from the stability of an iterated function system, this paper constructs a unified framework from discrete geometry to continuous spacetime, and then to particle physics and cosmology. The first part proves the necessity of the base and selects Calabi–Yau manifolds; the second part establishes a renormalisation group theory of recursive folding, realising a dimensional transition from 1 to 4; the third part computes Yukawa couplings on Tian–Yau manifolds and predicts the lepton mass ratio; the fourth part establishes discrete symmetries and a quasi‑Noether theorem. The framework provides testable predictions such as CMB non‑Gaussianity and signals from black hole evaporation. 本论文由四篇论文组合而成,但各自会保持分立性,以便于读者阅读。 主论文:从康托尔空间到卡拉比-丘流形:离散几何的顺向推导拆分论文I:从离散层级到连续时空:递归折叠的重整化群分析拆分论文II:Tian-Yau 流形上的 Yukawa 耦合与轻子质量比 206.768拆分论文III:离散几何中的对称性与守恒律:一个准诺特定理 整合摘要: 概括四部分的核心关联,而非简单拼接。例如: 本文从迭代函数系统的稳定性出发,构建了一个从离散几何到连续时空、再到粒子物理与宇宙学的统一框架。第一部分证明进制必然性并筛选出卡拉比-丘流形;第二部分建立递归折叠的重整化群理论,实现维度从1到4的跃迁;第三部分计算Tian-Yau流形上的Yukawa耦合,预言轻子质量比;第四部分建立离散对称性与准诺特定理。框架提供CMB非高斯性、黑洞蒸发信号等可检验预言。 整合关键词:discrete geometry, Calabi-Yau manifolds, renormalization group, Yukawa couplings, quantum gravity