Yeah, like Jonathan I don't see how proving one particular problem that's known to take at least exponential space is in \\(\text{NP}\\) would imply \\(\textrm{EXPSPACE} \subseteq \textrm{NP}\\).

I've never heard anything about Petri net reachability being \\(\textrm{EXPSPACE} \\)-complete. If it's true I wanna know!