Cosmic Structures and Minimal Complexity: Empirical Evidence from Mass and Field Ratios

This paper explores the universal principles governing cosmic organization, focusing on the scaling laws of mass (M1/3M^{1/3}M1/3) and magnetic fields (B1/4B^{1/4}B1/4), derived from the principle of minimal complexity. This framework asserts that natural systems evolve toward stability with minimal resource expenditure, creating predictable geometric relationships. Using data from solar system bodies and exoplanetary systems, the study validates these scaling laws and demonstrates their universality across gravitational and electromagnetic phenomena.

The research highlights the concept of perfect multiplicative coherence, which ensures consistent scaling relationships within and across systems, from planetary hierarchies to interstellar magnetic fields. Solar system data exhibit exact coherence, while exoplanetary systems reveal similar trends, with minor deviations providing insights into dynamic instabilities or observational gaps.

By bridging gravitational and electromagnetic domains, the study underscores the scale-invariant nature of these principles, suggesting their applicability to larger cosmic structures, such as galaxies and clusters. This work contributes to a deeper understanding of how the universe organizes itself through simple yet profound geometric constraints, offering predictive power and a unified framework for future explorations of cosmic stability and coherence.