  The goal of this note is to demonstrate that as soon as the hyper-diffusion
exponent is greater than one, a class of finite time blow-up scenarios
consistent with the analytic structure of the flow (prior to the possible
blow-up time) can be ruled out. The argument is self-contained, in spirit of
the regularity theory of the hyper-dissipative Navier-Stokes system in
turbulent regime developed by Grujic and Xu.
