  Studying the series expansion of the thermodynamic potential for the
hard-core N3 lattice-gas model, we provide evidence for a first-order
phase-transition with a finite jump in density and entropy, in agreement with
numerical transfer matrix calculations. The solid branch terminates at the
transition, while the fluid branch continues beyond the critical activity,
describing a meta-stable super-cooled fluid. It terminates with density 0.85
(relative to the closest packing density) and finite entropy per site. This
termination density is close to the random-closest-packing density of the
glassy state obtained for infinitely-fast cooling. The model thus exhibits a
thermodynamic meta-stable glassy phase with finite Edwards' compactivity.
