1 = 0: A Thermodynamic Alternative to the Navier–Stokes Equations via Extended 14-Moment Hyperbolicity and Scale-Space Regularization

For nearly two centuries, the classical Navier–Stokes equations have served as the foundational governing model of continuum fluid mechanics. Despite their engineering utility, the equations harbor unresolved mathematical pathologies—most notably the open question of finite-time blow-up of smooth solutions in three dimensions—and require empirical closure hierarchies to approximate high-Reynolds-number turbulence. In this work, we demonstrate that these pathologies are not intrinsic features of physical fluids, but mathematical artifacts resulting from treating an instantaneous local spatial derivative as a fundamental physical law. By enforcing the Local Thermodynamic Equilibrium (LTE) truncation (De = τmicro/τmacro → 0), the classical Newton–Stokes closure (τ dev = 2µDdev) discards the finite relaxation memory and non-local phase-space contraction of irreversible energy dissipation. We formulate a rigorous alternative grounded in the 1 ̸= 0 Non-Equivalence Principle: a dissipative continuum with strictly positive entropy production (σ > 0) cannot be topologically reduced to a memoryless sequence of equilibrium tangent projections. Expanding the state space to a 14-moment Extended Irreversible Thermodynamic (EIT) manifold M = {ρ, u, e, Π, τ dev, q} equipped with the trace-preserving, frame-indifferent corotational Jaumann derivative