Authors: Stergios Pellis
The Golden Function represents a novel, dimensionless framework for understanding the interrelations between fundamental constants, interactions, and structures across diverse scientific disciplines. Inspired by the golden ratio φ and fractal geometries, this function offers a unifying perspective on the mathematical and physical principles that govern the cosmos, from the quantum scale to cosmology, biology, and even human cognition. In this paper, we explore the foundational aspects of the Golden Function, examining its potential to unify disparate scientific fields such as particle physics, cosmology, biology, and mathematics under a single, coherent structure. We analyze its application in areas ranging from quantum mechanics to the dynamics of biological systems, and propose that the function can serve as a tool for predicting new phenomena, revealing previously unrecognized symmetries in nature, and enhancing our understanding of complex systems. By connecting fractality, scaling laws, and the fine-structure constant, the Golden Function opens up new avenues for interdisciplinary research, bridging the gap between abstract theoretical frameworks and empirical observations. Ultimately, this paper positions the Golden Function as a cornerstone in the pursuit of a unified theory of everything, highlighting its potential to reshape our understanding of the universe at all scales. The inverse fine-structure constant has long intrigued physicists due to its dimensionless nature and fundamental role in quantum electrodynamics. In this work, we propose a novel topological framework for its emergence based on the geometry of the Poincaré Dodecahedral Space (PDS) and the arithmetic of the golden ratio φ. We introduce the Golden Function: a φ-scaled summation of rational components that approximates the experimental value of fine-structure constant with high precision. Its structure mirrors the spectral distribution of the Laplace—Beltrami operator on PDS. We argue that this expression is not numerological, but an emergent topological eigenvalue arising from the compact, positively curved 3-manifold , where natural harmonic modes reflect φ-based fractal scaling. The use of φ—an irrational, dimensionless constant found in both mathematics and biology—bridges quantum microphysics and global spatial topology, suggesting a universal, scale-invariant architecture. We demonstrate that the first eigenmodes of the PDS Laplacian correspond quantitatively to the terms in the Golden Function and define constraints on physical constants, consistent with a holographic or topological quantum field theory framework. By embedding φ-scaling into the spectral topology, the fine-structure constant arises not as an arbitrary empirical number but as a consequence of the Universe’s fractal-harmonic and topological structure. We further propose a dimensionless derivation of fine-structure constant, grounded in the Golden Function, incorporating Euler’s number, the golden ratio, and circular constants. The model embeds a fractal golden torus inside 3-spheres, including the Poincaré dodecahedral space, to describe fundamental quantization and angular momentum states. Recursive golden spirals constrained within higher-dimensional topologies reveal the geometric origin of electromagnetic coupling, unifying topological quantization, conformal invariants, and toroidal harmonics in a cosmological—quantum framework.
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