Since the time of Kepler it is thought that the most efficient packing of monodisperse spherical grains is the face centered cubic (FCC) arrangement with a density of 74 % [1]. Thus, we might expect that spherical particles will tend to optimize the space they occupy by crystallizing up to this limiting density. Instead, granular systems of spheres arrest in a random close packing (RCP), which is not optimal but occupies ∼ 64% of space [2]. Previous studies have derived geometric statistical models to map the microscopic origin of the much debated 64% density of RCP [2–9]. However, the physical laws that govern its creation and render it the most favorable state for randomly packed particles remains one of the most salient questions in understanding all of jammed matter [3–5, 8]. For instance, while it is known that systems in equilibrium follow energy minimization and entropy maximization to reach a steady state, the mechanism by which RCP is achieved is much sought after. Here we propose a thermodynamic view of the sphere packing problem where the exper- imentally observed RCP can be viewed as a manifestation of a singularity in a first-order phase transition. Despite the inherent out-of-equilibrium nature of granular matter, the formation of a jammed crystal can be mapped to a thermodynamic process that occurs at a precise compactivity where the volume and entropy are discontinuous. We investigate mechanically stable packings ranging from the lowest possible volume fraction of random loose packing (RLP) [10] to FCC. We numerically generate packings of N =10,000 spherical particles of radius R = 100 µ m in a periodically repeated cube. Initially, we use the Lubachevsky-Stillinger (LS) [11, 12] and force-biased (FBA) [13] algorithms to generate amorphous configurations of unjammed hard-spheres fluids at infinite kinetic pres- sure and volume fraction φ$_{i}$ [6, 12] (see Appendix-Section I). While these configurations are geometrically jammed, they are not jammed in a mechanical sense since the particles do not carry any forces: the confining stress σ (not kinetic) is zero. In fact a key difference between granular materials jammed under external stress or gravity and hard-sphere fluids is that, in the former, each particle satisfies force and torque balance. In order to study mechanically stable packings characterized by a jamming transition we introduce interparticle forces via the Hertz-Mindlin model of normal and tangential forces allowing the particles to be soft but with a large Young modulus, Y . We then simulate the process of jamming by Molecular Dynamics (MD) simulations using previously developed methods [14] to compress the LS and FBA packings from φ$_{i}$ to a final jamming density, φ$_{j}$ . Ultimately, we obtain mechan- ically stable packings just above the jamming transition (in the limit of vanishingly small 2