Is random close packing a well-defined density
In plain words
Shaking or pouring identical balls into a box gives a disordered packing filling about 64 percent of the space, called random close packing. Whether this number is a true property of spheres or depends on how the packing was made is disputed.
Precise statement
For monodisperse frictionless spheres in $d = 3$ (and disks or bidisperse mixtures in $d = 2$), determine whether random close packing $\phi_{\mathrm{RCP}}$ (about 0.64 in $d = 3$) is a protocol-independent density, for example the density of the maximally random jammed state or a limit fixed by equilibrium crowding, given that jamming densities $\phi_J$ of frictionless packings vary with compression rate by a few percent (approximately 0.64 to 0.66 in 3D model systems). An answer is a precise definition of $\phi_{\mathrm{RCP}}$ that yields a unique number, with a derivation or numerical demonstration that it is independent of protocol, or a proof that no such definition exists.
What would settle it
A definition of random close packing whose value is shown, analytically or by simulations across many protocols, to be unique, or a demonstration that every candidate definition depends on protocol.
Status in the literature
Unverified note
Torquato, Truskett and Debenedetti argued in 2000 that RCP is ill defined (https://doi.org/10.1103/PhysRevLett.84.2064); a 2022 analytical prediction (Zaccone, https://doi.org/10.1103/PhysRevLett.128.028002) drew a published comment and reply, and closed-form RCP models for polydisperse disks continued to appear in 2025-2026.