Manifesto on the Completion of Classical Mechanics

This manifesto presents a timeless reconstruction of classical mechanics through the Universal Hamiltonian (UH), which incorporates the complex gauge symmetry and spatial potential energy (+) often excluded from traditional formulations. The classical Hamiltonian UH=(1/2)mv^2−GMm/r includes both gravitational attraction (−GMm/r) and expansionary repulsion (+GMm/r), resulting in UH=(1/2)mv^2−GMm/r +i(GMm/r).This theory restores the intrinsic phase equilibrium and bipolar structure of Universe.This complex formulation completes the ontological symmetry between real and imaginary components of dynamics, achieving mathematical and conceptual unification of classical physics. It establishes the foundation for a wave-based unified theory (Oscillation TOE), redefining all motion and energy as complex phase interactions in a gauge-symmetric space, beyond conventional time-dependent physics.Natural time independence and complex energy restoration will automatically solve long-standing problems in physics and mathematics.