  We present $O(\alpha_s)$ analytic predictions for event shape 1-jettiness
$\tau_1$ distribution aiming measurements in deep inelastic scattering process
at future Electron Ion Colliders. The result depends on conventional variables
$x$ and $Q$ as well as on $\tau_1$ and is relatively compact and easy to
implement for numerical calculation. Three different choices of axis, with
respect to which $\tau_1$ is measured are considered in the Breit frame. The
first is the one optimally adjusted to minimize $\tau_1$ and the second and
third are taken from anti-$k_T$ and Centauro jet algorithms defined with a jet
radius parameter $R$, respectively. We find that the first and second give the
same result at this order and are independent of $R$, while the third depends
on the radius. This fixed-order result provides a nonsingular contribution to
be combined with a singular log-resummed contribution to give the full spectrum
in $\tau_1$ space and also shows how fixed-order and resummation regions change
as a function of $x$ and $Q$.
