An open vertical container exposed to atmospheric pressure \(P_0\) contains three distinct layers of immiscible liquids in static equilibrium with densities \(\rho_1 < \rho_2 < \rho_3\). A uniform solid cylinder of length \(L\), cross-sectional area \(A\), and uniform density \(\rho_c\) (where \(\rho_1 < \rho_c < \rho_3\)) floats vertically in static equilibrium. The flat top face of the cylinder is submerged in the top liquid at a depth \(d\) below the free surface, while its flat bottom face rests in the bottom liquid. In terms of the given quantities and fundamental constants, which of the following is a correct expression for the absolute pressure \(P_b\) exerted on the bottom face of the cylinder?