The Navier-Stokes Equations as a Resolution Geometry Theorem: Deriving Fluid Dynamics as Momentum Transport on a Friction-Constrained Scaffold

This companion paper demonstrates that the Navier-Stokes equations—the governing laws of fluid dynamics—are not empirical observations of continuum mechanics, but necessary theorems of multi-ledger bookkeeping under finite capacity.

In Resolution Geometry, a fluid is a system tracking two coupled ledgers: Mass (identity count) and Momentum (identity flow). The system is constrained by Exclusion (finite slot capacity, leading to incompressibility) and Interaction Friction (receipt accumulation from shearing, leading to viscosity).

We derive the Navier-Stokes equations as the condition for balancing Inertial Transport (ledger movement) against Exclusion Cost (pressure) and Smoothing Cost (viscosity).

Crucially, this framework provides a geometric definition of turbulence: it is Resolution Saturation, where the rate of information transport (advection) exceeds the scaffold's capacity to smooth gradients (diffusion), forcing the geometry to fracture into fractal eddies to manage the overflow.