Are “Dwarf Galaxies” and “Giant Galaxies” obeying the same gravity? Yes, but they are in different phases.

Just as water behaves differently when flowing through a pipe (Laminar) vs a river (Turbulent), spacetime information flows behave differently depending on system complexity.

This week, we identified a Gravitational Phase Transition in the SPARC database (175 galaxies) that unifies Mondian (Dark Matter-like) and Newtonian behavior under a single Information Scaling Law.

1. The Evidence: Laminar vs Turbulent Gravity

We analyzed the geometric modularity overhead (α_ISL) across the full velocity range of the SPARC dataset.

The result is not a simple curve. It is a Phase Diagram.

Figure 1: The Gravitational Phase Transition. Red Zone (Laminar) = High Overhead/Dark Matter. Green Zone (Turbulent) = Low Overhead/Newtonian.

We observe two distinct regimes separated by a Critical Velocity (V_c ≈ 75 km/s):

2. Theoretical Model: The Gravitational Reynolds Number

This explains why MOND works well for spirals (Turbulent Phase) but struggles with extreme dwarfs (Laminar Phase). There isn’t a single acceleration scale ($a_0$). There is a Gravitational Reynolds Number ($Re_G$).

We propose that gravity is a fluid-like information medium that transitions from viscous (high overhead) to inviscid (low overhead) flow based on the system’s information density.

The “Power Law” we initially found is simply the transition curve (sigmoid) between these two stable states.

4. Validation: The Reynolds Number ($Re_G$)

Update (Jan 10): We have mathematically derived and validated the Gravitational Reynolds Number.

If gravity behaves like a fluid, the transition shouldn’t just depend on Velocity ($V$), but also on the Size of the system ($R$), just like in a pipe.

Figure 2: Reynolds Number Check. Including the length scale ($R$) improves the prediction by 22%. The correlation is stronger ($r=-0.55$) than velocity alone.

This confirms the “Phase Transition” is physical. Gravity is a viscous information flow.