 are repulsive.  0.  $\lim_{\varepsilon \rightarrow 0^+} \Delta \tilde{E}^{H^\varepsilon}_\eta (\gamma_x) = \Delta \tilde{E}^{H^0}_\eta (\gamma_x)$ for all $\eta \in \mathcal{N}( {{\mathbb R}}^d \times \{+,-\})$ and $\gamma_x \in  {{\mathbb R}}^d \times \{+,-\}$ such that both $\eta$ and $\eta + \delta_{\gamma_x}$ are outside the dynamically impossible set $