The Scale of Curvature: An Item-by-Item Mapping Proof of the Lambda-CDM Six Parameters to T64 Topological Curvature Invariants

The contemporary standard cosmological model, Lambda-CDM, relies on six fundamental free parameters to fit observational data from the cosmic microwave background, large-scale structures, and baryon acoustic oscillations, thereby describing the comprehensive evolutionary history of the universe. In contrast, Yuanxian Theory (YXT/T64) takes the 64-dimensional compact flat torus as the unique cosmic ontological topology, constructing a global physical framework with zero free parameters and pure topological a priori deduction backed by four core axioms: the True-Circle Self-Consistency Law, the Cosmic Factor Conservation Law, the Spacetime Uniqueness Law, and the Self-Referential Mind Field Generation Law. This paper completes a rigorous item-by-item correspondence within the Yuanxian theoretical framework, establishing a precise dimensional reduction mapping between the Lambda-CDM six parameters and the topological curvature invariants of T64. We prove from an ontological standpoint that every manually fitted, artificially adjusted "free parameter" in Lambda-CDM is essentially a projective value of a high-dimensional topological geometric invariant onto the 4D spacetime cross-section, entirely locked by the topological rigidity of T64 with zero adjustable degrees of freedom. Specifically, the Hubble constant is mapped to the lowest fundamental normal frequency; the total matter density to the zero-mode rigid topological constraint; the dark energy density to the global scalar curvature projective mean; the primordial spectral index to the inherent scaling index of the normal mode spectrum; the primordial perturbation amplitude to the intrinsic mode excitation amplitude; and the reionization optical depth to the interdimensional projective information attenuation coefficient. This work definitively eliminates the parameter entropy of the Lambda-CDM framework, upgrading empirical-fitting cosmology into an ontologically traceable, topologically rigid cosmology. It provides an irrefutable paradigmatic path for cosmology to ascend from "parameter tuning for data adaptation" to "ontological source tracing." 当代Lambda-CDM宇宙学标准模型依靠6个基础自由参数拟合宇宙微波背景、大尺度结构、重子声学振荡等观测数据,以此描述宇宙整体演化历史。与之形成鲜明对比的是,元宪理论(YXT/T64)以64维紧致平坦环面作为宇宙唯一本体拓扑,依托真圆自洽律、宇宙因子守恒律、时空唯一性律、自指心场生成律四大核心公理,构建起零自由参数、纯拓扑先验推导的全域物理体系。本文在元宪理论框架内完成逐项严格对应,建立Lambda-CDM六参数与T64拓扑曲率不变量一一对应的精准降维映射。 本文从本体论层面证明:Lambda-CDM里每一个可手动拟合、人为调整的“自由参数”,本质都是高维拓扑几何不变量在四维时空截面的投影取值,不存在可调自由度,全部被T64拓扑刚性先天锁死。具体而言:哈勃常数被映射为64维环面简正模最低基频;总物质密度参数映射为拓扑零模刚性约束量;暗能量密度参数映射为全域标量曲率投影平均值;原初谱指数映射为简正模频谱固有标度指数;原初扰动振幅映射为模态心场激发本征幅度;再电离光深则映射为跨维度投影信息衰减系数。本文彻底消解了Lambda-CDM体系的参数熵,将经验拟合型宇宙学升级为拓扑读数式刚性宇宙学,为宇宙学从“调参适配”到“本体溯源”提供了不可推翻的范式路径。