{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"e9841bd437d10a9b09d04b6040bc51998923a595978daef6202957953682c0c9","created":"2026-10-03T07:17:57Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"5d600958f9ce8bc9fb13fdcea7e05e687c34c5993e829ba5fed2f129f66b1261","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"bio.jamming-rigidity.random-close-packing","kind":"well-posed","literature_status":"contested","n":"1","parents":[],"plain":"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.","posed_since":"2000","precise":"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.","problem_ref":null,"references":"","settled_by":"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_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.","title":"Is random close packing a well-defined density","topic_ref":"e88cb77371bb7a86f0fbdb1f952ba3eab78bc8141039cb805db532ac7cced95b"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"dfe9310867e658596b421c2ddcd74064d48cf1e5eb329e3e70ee5c687fbd198c","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"aae60cd85ec7de689338dfeef59425d131728b3cad07b9d6c736c8e199a15d17","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"gRZffua9s7aCgnZybEvNtZtdSpt4U7-eMVn5lIlLNBZyqsnMjK0iwrcIipdV5ZKDHnLSkiaaUbMVvAipeT4PAA"},"schema":"pubphys.envelope/1"},"record_hash":"dfe9310867e658596b421c2ddcd74064d48cf1e5eb329e3e70ee5c687fbd198c","leaf_index":790}