$-small.  Proof: By Proposition \[diamond\], there exists a sequence $\langle s_\alpha\rangle_{\alpha<\kappa}\in \left(0^{<\kappa}\right)^\kappa$ such that for all $x\in 0^\kappa$, $\{\alpha\in E\colon x{\mathord{\upharpoonright}}\alpha=s_{\alpha}\}$ is stationary in $\kappa$. 