PFUSRC-051: The Mathematical Reduction of the I Ching Constancy as the Foundation, the Trinity as the Substance, and Change as the Projection

This paper carries out a systematic mathematical reduction of the I Ching within the PFUSRC topological ontology framework and puts forward three core theses. First, the core essence of the I Ching lies not in "change" but in "constancy". Constancy refers to the Trinity: one unified cosmos, one fundamental logic, and one self-consistent topological living body. All phenomenal transformations are projections of the constant noumenon onto the manifest layer, and simplicity serves as the encoding form of the noumenon. Second, the eight trigrams are neither divination marks nor philosophical metaphors. They are symbolic records of the distribution of "explicit existence and gap field" in three-dimensional space, established by ancient observers based on the PFUSRC Unary Binary-State Topological Encoding. The solid line corresponds to the explicit topological primitive ⊮, and the broken line stands for the implicit gap field H^{0}. Three lines form 3D encoding (2^{3}=8), while six lines compose six-dimensional state encoding through inner and outer trigrams (8×8=64). Third, the River Chart, Luo Writing, the Great Extension Number, and core arguments of the Xici Commentary can be precisely mapped to key PFUSRC topological constants including the 45° triple coaxial bicone, the 12/11 topological gauge ratio, the 55 steady-state reference nodes, Ψ-Ξ anchoring and the \beta_{1} global operator. This paper does not deny the historical and traditional value of the I Ching, but points out that later Confucian scholarship only preserved the textual projection system and lost its original topological mathematical core. Confucius’s principle of "transmitting without creating" maintained textual inheritance yet caused a rupture of noumenal mathematics. Neo-Confucianism of the Song and Ming dynasties further solidified the circulating dynamic trigram sequence into a static hierarchical framework. Using modern topological language, this paper reconstructs the unique pre-Qin cosmic geometric model and reconnects the native first-principles academic lineage interrupted for more than two thousand years.