  In this paper, we prove the closure ordering conjecture on the local
$L$-parameters of representations in local Arthur packets of
$\mathrm{G}_n=\mathrm{Sp}_{2n}, \mathrm{SO}_{2n+1}$ over a non-Archimedean
local field of characteristic zero. Precisely, given any representation $\pi$
in a local Arthur packet $\Pi_{\psi}$, the closure of the local $L$-parameter
of $\pi$ in the Vogan variety must contain the local $L$-parameter
corresponding to $\psi$. This conjecture reveals a geometric nature of local
Arthur packets and is inspired by the work of Adams, Barbasch, and Vogan, and
the work of Cunningham, Fiori, Moussaoui, Mracek, and Xu, on ABV-packets. As an
application, for general quasi-split connected reductive groups, we show that
the closure ordering conjecture implies the enhanced Shahidi conjecture, under
certain reasonable assumptions. This provides a framework towards the enhanced
Shahidi conjecture in general. We verify these assumptions for $\mathrm{G}_n$,
hence give a new proof of the enhanced Shahidi conjecture. At last, we show
that local Arthur packets cannot be fully contained in other ones, which is in
contrast to the situation over Archimedean local fields and has its own
interests.
