Passive scalars advected by three-dimensional Navier-Stokes turbulence exhibit a fundamental anomaly in odd-order moments because of the characteristic ramp-cliff structures, violating small-scale isotropy. We use data from direct numerical simulations with grid resolution up to $8192^3$ at high P\'eclet numbers understand this as scalar diffusivity, $D$, diminishes, or Schmidt number, $Sc = \n...