Universal Magneto-Mechanical Particle Dynamics: A Scale-Invariant Framework for Quantum and Cosmic Phenomena

We present a universal particle dynamics model describing the equilibrium displacement of magnetically responsive particles with momentum-dependent modulation. Starting from first principles and incorporating a novel scale-invariant coupling constant α0 ≈ 10−42, we derive a displacement formula that successfully predicts phenomena across 40+ orders of magnitude: from subatomic muon g − 2 anomalies to galactic-scale rotation curves and gravitational lensing. This framework provides a mechanistic alternative to dark matter while resolving persistent tensions in precision particle physics measurements