A Cosmology of Geometric Intent and the Solar Orbital Registry

This paper presents a statistical and hydrodynamic audit of polar polygonal structures on the Gas Giants. We identify a correlation between planetary orbital index (I) and atmospheric wavenumber (N) that exceeds the threshold for random occurrence (P < 0.002). By integrating recent hypotrochoidal flow models (Constantin and Johnson, 2025) with magnetohydrodynamic (MHD) resonance theory, we propose that these geometries are not stochastic weather events but phase-locked signals indicative of a Solar Orbital Registry. We utilize Shannon Information Theory to quantify the Mutual Information of the solar system's arrangement (I(O; G) ≈ 3.0 bits) and identify Earth (I = 3) as an "Unregistered Node" due to scale-height limitations. The paper concludes with a falsifiable prediction: that the unmapped poles of Uranus (I = 7) will exhibit a stable Heptagonal standing wave, verifiable by the upcoming Uranus Orbiter and Probe (UOP).