Physical Geometry: Quantum Mechanics I - Action, Holonomy, and the Geometry Underlying Quantum Mechanics

Quantum mechanics is formulated in terms of complex phase and action-dependent amplitudes. In this work, quantum phase is identified with the holonomy of a geometric connection, and Planck's constant appears as the conversion scale between geometric transport and physical action. This provides a geometric formulation of quantum kinematics in which phase accumulation, noncommutativity, and quantization arise naturally from connection geometry and topology. This paper is Part I of the Physical Geometry Quantum Mechanics series, which develops a geometric framework for quantum mechanics based on holonomy and transport structure. Subsequent papers develop operator representations and dynamical structure. This Zenodo record establishes priority and archival timestamp. Public release via arXiv is in progress.