  We address consequences of strong tensor and weak spin-orbit terms in the
local energy density functional, resulting from fits to the $f_{5/2} - f_{7/2}$
splittings in $^{40}$Ca, $^{48}$Ca, and $^{56}$Ni. In this study, we focus on
nuclear binding energies. In particular, we show that the tensor contribution
to the binding energies exhibits interesting topological features closely
resembling that of the shell-correction. We demonstrate that in the extreme
single-particle scenario at spherical shape, the tensor contribution shows
tensorial magic numbers equal to $N(Z)$=14, 32, 56, and 90, and that this
structure is smeared out due to configuration mixing caused by pairing
correlations and migration of proton/neutron sub-shells with neutron/proton
shell filling. Based on a specific Skyrme-type functional SLy4$_T$, we show
that the proton tensorial magic numbers shift with increasing neutron excess to
$Z$=14, 28, and 50.
