The Origin of Complex Spacetime, Volume II Part I: General Mathematical Foundations

        This volume constitutes the logical backbone of the five-volume series The Origin of Complex Spacetime. Part I establishes the rigorous mathematical framework of the Degeneration Theorem—the proof that when the characteristic energy of a physical processfalls within a specific window, the complete PanGu primordial equation degenerates inorthogonal subspaces to general relativity, the Standard Model gauge field theory, andquantum mechanics.Chapter 1 presents the strict mathematical framework: the Low-Energy ImaginaryPart Freezing Theorem, which proves that the imaginary part fluctuation field acquires atopological mass meff ≈ 3.17 MeV from BCC lattice discretization, exceeding the theory’sultraviolet cutoff EUV ≈ 1.12 MeV and rendering it dynamically frozen across the entireapplicable energy regime. The Wilsonian complex path integration procedure formallyintegrates out the frozen imaginary part field, yielding the low-energy effective action.The precise energy-scale boundaries of the standard degeneration window E ∈ [μmin,Λ]are determined from first principles, and the complete three-regime physical picture isestablished.Chapter 2 converts the mathematical framework into a standardized four-stage deduction template—degeneration limit mathematical operations, step-by-step simplification calculus, core degeneration conclusion, and pre-embedded failure boundary clues—providing a unified logical framework for all seven degeneration proofs in Part II.V1.0 Strengthened Foundations: In this official release, the Degeneration Theorem receives rigorous theorem-level reinforcement archived in the Computational Handbook Appendices—E Series Supplemen