From a (3,3) Pseudo–Kähler Geometry to Quantum Uncertainty: A Self-Contained Framework

We present a unified construction that begins with a six-dimensional pseudo–Kähler manifold of signature (3,3), proceeds through a “real–imaginary” split and a bridge (“wormhole”) projection, and ends by deriving standard quantum mechanical structures—wavefunctions, operator commutators, tunneling amplitudes, and the uncertainty principle—from purely geometric data. We combine symbolic checks (via Sympy) and numerical sandbox experiments (Gaussian states, double-peak interference, rectangular-barrier tunneling) to demonstrate full consistency and to locate the geometric origin of non- commutativity.