Chapter 1 From 0 Dimensions to 4 Dimensions: The Dimension Generation Theorem

Axiom 0.1 (Imaginary Origin): In the 0-dimensional pre-geometric substrate I₀, only the phase-reversal operator i exists, satisfying i² = −1; it carries a 4-periodic symmetry and can generate a global U(1) gauge structure. No pre-given manifold, spacetime coordinates, or metric exist. Axiom 0.2 (Euler-Spiral Asymptotic Condensation). The topological generator E(θ) = e^(iθ) Γ(1/2 + iθ/2π) As θ → ±∞, the function exhibits asymptotic condensation behavior, defining the asymptotic condensation skeleton E₀. Note: Γ(1/2 + iz) possesses only asymptotically oscillatory decay as z → ±∞ and does not converge to a strict limit; E₀ is a custom asymptotic skeleton object of the theory, not a limit point of the function.