TITLE:
Emergent Golden Ratio Geometries in the Simulated Unified Resultant Amplitude Method: Bridging Wave Superpositions to Cuboctahedral Symmetries in Unified Physics
AUTHORS:
Shawn P. Guillory
KEYWORDS:
Waves, Golden Ratio, Fractals, Polyhedral, Unified Theory, Fine-Structure Constant
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.2,
February
2,
2026
ABSTRACT: This study presents a conceptual and geometrically motivated exploration of structured wave superposition using the Simulated Unified Resultant Amplitude Method (S-URAM), with particular emphasis on emergent hexagonal structures and their relation to the cuboctahedron in contemporary unification efforts. Through the application of radial wave overlays, critical intersection points produce configurations whose proportions naturally conform to the golden ratio (
φ
). Symmetric reflection of these patterns exhibit fractal-like scaling behavior comparable to the second iteration of the Koch snowflake, indicating inherent recursive self-similarity. Extending to three-dimensional cuboctahedral symmetry, phenomenological expressions are developed for the inverse fine-structure constant, the weak mixing angle, and the strong coupling constant—interpreting parameters and their refinements as arising from golden-ratio phase constraints, chiral asymmetries, volumetric corrections, and edge-multiplicity scaling. These results suggest a direct geometric linkage between S-URAM wave dynamics, polyhedral symmetry, and central concepts in unified physics—including Einstein field equations, grand unified theories, and quantum gravity & holographic mass frameworks. While the present work does not claim a replacement for established theories, by highlighting scalable, self-similar geometries that echo natural constants and structures, this approach offers fresh conceptual insights into bridging quantum mechanics, general relativity, and fractal descriptions of spacetime.