\phi_\mathbb{B}^{\mathrm{ GRC}} \big( g\cdot \mathds{0}_{\mathscr{M}(\Delta, \mathbb{V}(\mathbb{B}_0))} \phi_{\mathbb{B}_0}^{\mathrm{ GRC}}(f|\cdot)  \big|\omega_{\mathbb{B}^c}  \big) \phi(\mathrm{d}\omega)