Emergence of Physical Structures from Geometric Resonance Fields

Emergence of Physical Structures from Geometric Resonance Fields The Emergent Resonance-Brane (ERB) model proposes a reformulation of particle physics and cosmology in which matter, symmetries, and spacetime dynamics appear as emergent properties of a discrete complex resonance field defined on a lattice. The central idea of this work is that parameters traditionally treated as fundamental constants of the Standard Model may arise from the topology and geometry of the underlying resonance field. In particular, we present numerical evidence that the hierarchical structure of the Cabibbo-Kobayashi-Maskawa (CKM) matrix can emerge from geometric overlap integrals of localized resonance modes (vortices). The model reproduces the experimental quark mixing pattern with a mean absolute error (MAE) of 0. 001786. Within this framework CP violation, quantified by the Jarlskog invariant (J 3 10^-5), appears as a geometric constant associated with the fundamental phase of the resonance field. The ERB framework further suggests a cosmological interpretation: localized energetic defects of the resonance field generate gravitational effects resembling dark matter, while diffuse background fluctuations produce a weak large-scale expansion component analogous to dark energy. By providing the complete simulation code used in this study, the work establishes a transparent and reproducible basis for exploring this unified resonance-based framework. The ERB model therefore offers a potential bridge between particle physics and cosmology based on the simple principle of geometric resonance.