Complex Sphere Universe: Gauge-Symmetric Natural Dynamics and the Oscillatory Nature of Existence

1. Declaration of Natural Dynamics Existence is oscillator; it oscillating energy. All beings are complex oscillators, composed of mass energy (real), spatial potential (imaginary), and phase motion (natural dynamics). The phase axis is natural dynamics itself. It is a geometric path system that enables harmonious movement without time, governed by energy balance (gauge symmetry) and the principle of least action. 2. The Structure of the Spherical Complex Universe General expression of the complex oscillator: Ψ = ρ ⋅ eiϕ • ρ : Energy density or spatial mass distribution (real part) • ϕ : Phase angle or spatial phase state (imaginary part) • Ψ : Complex oscillator state function