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A decades-old proposal that all distinct packings are equally probable in granular media has gone unproven due to the sheer number of packings involved. Numerical simulation now demonstrates that it holds — precisely at the jamming threshold. In the late 1980s, Sam Edwards proposed a possible statistical-mechanical framework to describe the properties of disordered granular materials1. A key assumption underlying the theory was that all jammed packings are equally likely. In the intervening years it has never been possible to test this bold hypothesis directly. Here we present simulations that provide direct evidence that at the unjamming point, all packings of soft repulsive particles are equally likely, even though generically, jammed packings are not. Typically, jammed granular systems are observed precisely at the unjamming point since grains are not very compressible. Our results therefore support Edwards’ original conjecture. We also present evidence that at unjamming the configurational entropy of the system is maximal.