Navier–Stokes as relational difference redistribution: A mechanism model for incompressible flow under closure constraints

This manuscript reformulates Relational Dynamics of Difference (DRD) as a mechanism model for interpreting incompressible Navier–Stokes flow from the perspective of the Relational Geometry Model (RGM). The primitive field $D(x,t)$ stores accumulated relational difference, its rate P=∂tDP=\partial_tDP=∂tD represents active redistribution, and $\Pi$ enforces incompressibility. Classical incompressible Navier–Stokes is recovered when explicit memory restoration and network friction are suppressed. The extension admits a fixed-regime energy identity, corrected modal phase diagnostics, a vorticity formulation, threshold regime activation, and a falsifiable finite-band modal-ringing prediction distinguishing DRD from both Newtonian relaxation and single-relaxation viscoelasticity. ROSI is treated as a possible future discrete realization, not as an assumed derivation.