Geometric Dynamics Reconstruction of Wave-Particle Duality

Based on the Geometric Dynamics Unifed Theory(GDUT), this paper attempts to provide a classical physical interpretation framework for wave-particle duality and the intrinsic properties of particles from the perspectives of three-dimensional continuum me-chanics and geometric topology. We propose that a wave packet can be regarded as a local stress micro-element in the 3D spatial medium, with its energy density evolving proportionally to the fourth power of the inverse wavelength. Considering that the spatial medium possesses non-Newtonian rheological proper-ties, continuous nonlinear stiffness hardening occurs as energy density increases. When the local stress sur-passes the critical threshold of the prolate-to-oblate ra-tio (the ratio of bulk modulus to shear modulus), the wave packet undergoes a Mo¨bius topological folding,thereby undergoing a phase transition from a deforma-tion wave to a physical particle with rest mass. Furthermore, this paper attempts to derive the spin(originating from Mo¨bius double-cover and classi-cal pressure-relief rotation), mass (integral locking of deformation energy within topological boundaries),fnite-range truncation mechanism of gravity, and the geometric contraction ratio of electric charge. Finally,the wave-particle phase transition equation is assem-bled, incorporating nonlinear hardening, the Planck cutoff, and the quartic ejection mechanism. This pa-per aims to serve as an introduction and expects this hydrodynamic model to provide a purely geometric and fuid-mechanical reference for resolving the di-vergences in quantum feld theory and the paradox of wave function collapse, while proposing several ex-ploratory directions that can be tested by future exper-iments.