  In this paper, we prove that the net of transition chain is $\delta$-dense
for nearly integrable positive definite Hamiltonian systems with 3 degrees of
freedom in the cusp-residual generic sense in $C^r$-topology, $r\ge 6$. The
main ingredients of the proof existed in \cite{CZ,C17a,C17b}. As an immediate
consequence, Arnold diffusion exists among this class of Hamiltonian systems.
The question of \cite{C17c} is answered in Section 9 of the paper.
