Lava-Void Cosmology Pillar 4: Planetary Science (v3.0)

Subtitle: From Lava Filaments to Worlds - Mesoscale Structure and the Nomadic Filter This document establishes the third, comprehensive revision of the fourth pillar of Lava-Void Cosmology (LVC). This update integrates Planetary Formation as an explicit mesoscale bridge, linking galactic fluid clustering to the habitability phase transitions and astrobiological outcomes previously established. 1. Protoplanetary Disks as Fluid Instabilities In the LVC paradigm, disks are modeled as transient high-density regions within galactic lava streams. We derive disk architecture using the Effective Péclet Number ($Pe_{disk} = \sigma_{gal} L_{disk}^2 / \nu_{fluid}$), explaining observed ring-gap substructures as results of inherited cosmic viscosity rather than ad hoc planetary perturbers. 2. Hydrodynamic Torque & Migration We provide a full derivation of planetary migration torques, emphasizing the role of viscosity saturation in the LVC fluid: Type I: Linear regime governed by Lindblad and Corotation torques. Transitional/Type II: Gap-opening and viscous coupling. Type III: Runaway regimes suppressed by high-viscosity damping. Rogue Ejection: Shear-modulated ejection paths that populate the galactic halo with "Nomadic Lifeboats." 3. Case Studies & Demographics Solar System Analogs: Reconstructing the divergent tracks of Jupiter (Type II) and the ice giants (Type I/Transitional). Exoplanet Signatures: Predicting the suppression of close-in giants in high-viscosity regimes and an overabundance of Saturn-mass rogue planets. 4. Interactive Proof System: Includes the Planet Formation & Migration Simulator (lava_void_planetary_dashboard_ultra-v3.html), which allows users to compare standard vs. LVC-enhanced viscosity tracks for ice giants and Jupiter analogs. The complete mathematical derivation and extended discussion for Lava-Void Cosmology and all pillars can be found on https://www.mylivingai.com/