Recoverable systems and the maximal hard-core model on the triangular lattice

In a previous paper (arXiv:2510.19746), we have studied the maximal hard-code model on the square lattice ${\mathbb{Z}}^2$ from the perspective of recoverable systems. Here we extend this study to the case of the triangular lattice $\mathbb{A}$. The following results are obtained: (1) We derive bounds on the capacity of the associated recoverable system on $\mathbb{A}$; (2) We show non-uniqueness of Gibbs measures in the high-activity regime; (3) We characterize extremal periodic Gibbs measures for sufficiently low values of activity.