_0}.$$  0.  If also $\lambda > \lambda^*$, where $$\lambda^* := \inf \left \{ \lambda > 0 \,:\, \sum_{\gamma^+_x : d_0(0, \text{supp}(\gamma^i_x)) \leq 0} |\gamma^+_x| \left[\frac{Z^0(\text{Int}_0(\gamma^+_x))}{Z^+(\text{Int}_0(\gamma^+_x))}\right]e^{-\Phi_