Part I of Volume II serves as the universal mathematical toolkit for the entire five-volume series. Inheriting the axiomatic framework of Volume I (C-layer primordial theory), this volume constructs a complete system covering Cl8,C Clifford algebra, discrete topology of BCC lattices, complex tangent bundles and complex fiber bundles. It unifies the full set of algebraic rules for non-Hermitian complex bilinear metrics, alongside general formulas for complex connections, covariant derivatives and complex curvature tensors. All terminology and the LIA single-length dimensional system are fully consistent with Volume I, and a cross-volume formula numbering standard is established for all five volumes. This part only contains fundamental mathematical definitions, core identities and key derivations; physical equivalence deductions including low-energy degradation theorems and (Simp.) approximate equations are exclusively placed in Part II of this volume. The mathematical tools in this volume provide a unified computational foundation for particle spectrum, cosmology and experimental engineering deductions in Volumes III, IV and V. Full high-energy primitive equations are referenced from Volume I, while low-energy simplified equations are sourced from Volume II Part II