Scale Invariant Field Organization as a Subset of the Universal Quantum Foam Hypothesis: Atoms and Galaxies as Homologous Field-Mechanical Realizations

This preprint addresses a specific sub-area of the Universal Quantum Foam Hypothesis (UQSH), focusing on the mechanical symmetry between micro- and macrocosmic structures. Building upon the ontological framework published on January 6, 2026 (based on the work from November 2025), it outlines the functional homology between atoms and galaxies. The paper describes the atom as a local field node and electrons as stable vortex modes of a dynamic medium. By applying scale-invariant field mechanics, a unified understanding of time and entropy is developed, using the field's reorganization rate as a central metric. This document serves as an extension of the existing UQSH framework, bridging the interpretative gap between the quantum level and large-scale cosmic structures.