 \sum_{T} \sum_{({\mathbf x}_0, {\mathbf y}) \in \Omega(T)} \varphi({\mathbf x}_0,{\mathbf y}) \varphi_{{\mathrm{KM}}} \left( \sqrt{v_0} x_0+ \frac{y \cdot v'_{00} }{ \sqrt{v_0}} \right)\wedge { \mathfrak{g}}(ya_0^*)   