The constructed vector field, foliation, potential, etc., depend on the pair $(\lambda,\nu)$, as well as on the regularization parameters $h,h^{\vee}$. But to simplify the notations for $\mathfrak{X},\mathcal{F},\Phi,\Phi^{\mathrm{sm}}$ we will often leave only those indices which are important in a current consideration and omit the rest when there is no confusion possible.