5.11 Geometric Hilbert Expansion — Navier-Stokes Equations

G5 has derived the compressible Euler equations from the information field dynamical equation via the first order of the Hilbert expansion. This article (G6) advances the expansion to second order, rigorously deriving the incompressible Navier-Stokes equations. Core results: (1) geometric shear viscosity , bulk viscosity ; (2) geometric thermal conductivity ; (3) geometric Prandtl number . All coefficients are locked by spectral rigidity, with no external parameters. The mathematical structure is completely parallel to Deng-Yu's derivation of the Navier-Stokes equations from the Boltzmann equation. **Keywords**: Second-order Hilbert expansion; Navier-Stokes equations; geometric viscosity; geometric thermal conductivity; Prandtl number; solvability condition; low Mach number limit