Coherence Density and Gradient Dynamics Across Planetary and Galactic Scales

This upload contains a two-paper series presenting a coherence-based framework for quantifying organized structure in astrophysical systems through a dimensionless measure called coherence density (ρ_c). Paper I: Coherence Density and Gradient Dynamics in Astrophysical Systems: Definition, Governing Equation, and Boundary Predictions Defines ρ_c by integrating magnetic, gravitational, thermal, and rotational observables into a canonical dimensionless metric, then derives the RMAχτ Gradient Invariant — a first-order differential law governing how ρ_c evolves spatially under suppression, regeneration, and entropy recycling. Validated against the near-Earth suppression potential and heliospheric boundary location (~122 AU, consistent with Voyager measurements). Includes worked examples spanning planets, moons, and a dwarf planet, and introduces a coherence-based reframing of habitability assessment. This paper consolidates and supersedes the original Papers I and II of the three-paper series (Zenodo: 10.5281/zenodo.18165641). Paper II: Galactic Coherence Gradients: Empirical Validation of the RMAχτ Invariant in the Milky Way Applies the gradient law to Milky Way stellar density data, demonstrating that the same dynamics governing planetary coherence boundaries reproduce galactic-scale equilibrium structure. The equilibrium threshold is identified at 7.8 ± 0.4 kpc with 82% statistical closure across parameter space. Together these papers form a continuous theoretical arc: Definition + Dynamics (ρ_c and RMAχτ) → Empirical Validation (Galactic Gradients). Each paper can be read independently, but the set is designed as a cohesive two-part work. Readers of the original three-paper series should note that Papers I and II have been consolidated into the new Paper I, with canonical dimensionless ρ_c now the authoritative formulation throughout.