Geometric Dynamics of Matter: A Unified Spectral Framework from Strong Interactions to Chemical Bonding

This work presents the second part of a research series on the geometric dynamics of matter. Following the establishment of the foundational spectral operator D̂ on the volume-preserving diffeomorphism group SDiff(M) [Link/Reference to Part I], this study investigates the application of the framework to molecular chemistry and condensed matter systems. We introduce the Geometric Stress Relaxation Algorithm (GSRA), a parameter-free computational paradigm with O(N log N) complexity, to quantitatively derive chemical bonding, the periodic law, and nuclear-to-molecular phase transitions from first principles. Our results identify chemical reactivity as a manifestation of topological entropy reduction and provide specific experimental predictions for high-pressure topological fracture and gravitational modulation of nuclear forces.