DRC-05: Dissipation-Range Reservoir Closure, Low-Mode Driver Packets, Boundary Residence, and Forcing-Level Viscous Coercivity

Dissipation-Range Reservoir Closure, Low-Mode Driver Packets, Boundary Residence, and Forcing-Level Viscous Coercivity

DRC-04 reduces the core of the main dynamic residual to R_DISS∪R_DIL. The dissipation residual contains low-mode-driver dominance, forcing in the transition band around Q(t), a large dissipation-boundary span Q_I^+-J, and repeated high-frequency renewal in the deep-dissipation part already proven viscosity-small. This round asks whether these are really distinct reservoir mechanisms — the answer is: no. Using the Cheskidov–Shvydkoy dissipation-wavenumber structure, proves that once the deep high-frequency sector already shown viscously absorbable by DRC-03/04 is removed, the remaining quadratic vorticity forcing is controlled by a strong low-mode vorticity/gradient driver multiplied by a high-frequency strain-gradient state. A strong renewal packet must therefore either carry a quantitative low-mode driver-action packet, or reveal an even larger, earlier high-frequency state, forcing ancestry re-rooting. Repeated backtracking to a fixed smooth early time region forces a driver-action ancestor. Also proves a boundary-height residence theorem: a large dissipation-boundary span can only sustain an exponentially short normalized residence unless it pays a large driver action. R_DISS is therefore absorbed into a standard low-mode driver action (not proven impossible), and the main unresolved dynamic reservoir residual is reduced to R_DIL.