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.
Categories: math.CO cs.DM cs.IT math.IT math.PR