The intersection of local Arthur packets for even orthogonal groups and applications

We give algorithms to explicitly compute local Arthur packets and their intersections for even orthogonal groups $G_n$ over $p$-adic fields using extended multi-segments. In addition, we provide an algorithm which determines whether a representation of $G_n$ lies in a local Arthur packet. As applications, these results are used to identify distinguished parameters, prove the closure ordering conjecture, the enhanced Shahidi conjecture, the weak local Arthur packet conjecture, and the good parity unitary dual conjecture for $G_n$.