pattern of Fig. \[Fig:Lattice\_half\]. The possibility of a magnetic ground state in such a geometry is supported by exact results, such as Tsunetsugu’s theorem [@Tsunetsugu97] for the KLM, and Lieb’s theorem for the Hubbard model [@lieb89; @lieb89err; @Costa16]. The former is particularly relevant in this case, owing to the close relationship between PAM and KLM. Tsunetsugu showed that the ground state of the KLM on a bipartite lattice and at half filling has total spin $S=|N_\mathcal{A}-N_\mathcal{B}|/2$, where $N_\mathcal{A}$ and $N_\mathcal{B}$ are the number of sites in sublattices $\mathcal{A}$ and $\mathcal{B}$, respectively. In this theorem, the localized spins are also included when counting the number of sites in each sublattice, with their labels (i.e. belonging to $\mathcal{A}$ or $\mathcal{B}$) depending on the sign of the Kondo interaction. There is no assumption of translational symmetry in this result; missing sites can be randomly located. Although this theorem was proved for the KLM, one might expect a similar behavior in the closely-related PAM. If so, the total spin of the PAM in the half depleted lattice of Fig. \[Fig:Lattice\_half\] should be finite, i.e. a ferromagnetic ground state. Our goal here is to confirm this conjecture within unbiased methods, and, more importantly, quantify the 