Physical Geometry: Quantum Mechanics III — Amplitudes, Interference, and Probability from Transport Geometry

This paper develops the geometric origin of amplitudes, interference, and probability within the holonomy-based transport framework introduced in Physical Geometry: Quantum Mechanics I–II. Amplitudes are interpreted as holonomy weights associated with transport configurations, interference arises from the composition of alternative transport paths, and probability emerges as a geometric invariant of transport compatibility. The squared-norm structure is shown to follow from linearity, phase invariance, and consistency under composition, without requiring probabilistic postulates or measurement axioms. This work completes the representational foundations of quantum mechanics within the Physical Geometry framework. This Zenodo record establishes priority and archival timestamp. Public release via arXiv is in progress.