We present an operational reformulation of the three-dimensional incompressible Navier-Stokes equations in which nonlinear dynamics are treated as primary operations rather than field objects. The nonlinearity is identified as an irreducible triadic (Ω_3) threading process in Fourier space, while viscosity acts as a strictly absorbing operation with quadratic scale dependence. We introduce a spectral depth entropy functional that quantifies operational depth (energy migration to fine scales) and derive an entropy production inequality showing linear triadic amplification versus quadratic viscous suppression. We show that global regularity within the continuum envelope is equivalent to closure of a single, scale-local Ω_3 entropy inequality. The paper does not claim a proof of regularity; rather, it isolates the unique remaining obstruction in a form that makes its resolution structurally inevitable.