Equation of state for hard sphere fluids across the stable and metastable regimes

We review selected equations of state (EOSs) for three-dimensional hard-sphere fluids and revise a closed-virial construction to describe the stable and metastable disordered states. The equation preserves the prescribed coefficients B2-B11, uses a linear continuation constrained by estimates of B12-B16, and imposes a simple pole at the representative maximally random jammed packing fraction ηp=0.637. The pole is a modeling assumption for a disordered continuation and is not identified with an exact singularity of the equilibrium virial series. The remaining parameters are fitted to the high-density subset of the simulation data of Pieprzyk et al. [Phys. Chem. Chem. Phys. 21(13), 6886 (2019)]. The overall average absolute relative deviation is 0.022 36% over their 100 data points. With unchanged parameters, the deviation is 0.005 874% over 50 points from Davidchack and Laird [J. Chem. Phys. 157(7), 074701 (2022)]. Agreement with the high-order coefficient estimates is assessed as a construction consistency check. Comparisons distinguish the information used to determine each EOS from its subsequent performance. The resulting equation combines prescribed virial inputs, a representative disordered end point, and small pressure deviations over the tested range, while retaining a phenomenological high-order continuation.