Causal Frequency Propagation and Nonrecycling Diagnostics in Three-Dimensional Navier–Stokes

We develop a target-native diagnostic framework for three-dimensional incompressible Navier-Stokes dynamics that distinguishes persistence of existing high-frequency structure from genuine nonlinear source creation. The paper establishes an Eulerian packet persistence-versus-source-expenditure dichotomy, a fixed low-mode DQ probe frame, a source-frequency metric, and an oriented logarithmic frequency barycenter whose purely viscous contribution has a non-positive covariance sign. An exact smooth unforced shear family proves that normalized fixed-probe projective action cannot be universally bounded by viscosity, time horizon, initial kinetic energy, and full-lifetime viscous dissipation alone. Theorem 4.1 and its selected supporting core have been kernel-verified in Lean 4.24.0 with mathlib v4.24.0. The full manuscript has not been formalized in Lean. This preprint does not establish finite-time blowup or global regularity for the unforced three-dimensional Navier-Stokes equations and is not claimed as a solution of the Navier-Stokes Millennium Prize Problem. DOI reserved prior to publication: 10.5281/zenodo.22700084.