{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"5b1201556592d7b4d6dd5b15519a2f82e68ed508e7c4be3c0f9bc28f975a8e4c","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["94d3280305428cfa8d5d0dbda4edd28da33099d579a573e80fe87bd7be3f4765","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"93f71c70a726ecb9366330591438fa04854fe473e3d029d13869b8abe4113520","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"bio.jamming-rigidity.gardner-finite-d","kind":"well-posed","literature_status":"contested","n":"2","parents":[],"plain":"Mean-field theory predicts that a glass compressed deep into its solid state undergoes a further transition, the Gardner transition, where each glassy state splits into many nearly equivalent sub-states. Whether this transition survives in real three-dimensional glasses or is only a smooth crossover is unknown.","posed_since":"2014","precise":"In the $d \\to \\infty$ solution for hard spheres, a stable glass becomes marginally stable at a pressure $p_G$ through full replica symmetry breaking (a hierarchy of sub-basins). For $d = 3$ hard- or soft-sphere glasses, determine whether the caging susceptibility $\\chi_{AB}$ (fluctuation of the mean-square distance between two copies of the same glass) diverges in the thermodynamic limit at finite $p_G$, or stays finite. Perturbative arguments suggest the transition may be destroyed below $d = 6$, while a nonperturbative fixed point found in $d < 6$ would allow it.","problem_ref":"94d3280305428cfa8d5d0dbda4edd28da33099d579a573e80fe87bd7be3f4765","references":"","settled_by":"Finite-size scaling of $\\chi_{AB}$ in well-equilibrated $d = 3$ glasses showing divergence or saturation, or a renormalization-group proof of existence or absence.","status_note":"Simulations in $d = 2 \\text{ and } 3$ report Gardner-like crossovers (2016-2023), including a generic dynamic Gardner crossover in compressed hard disks (Liao et al., PNAS 2023); field theory is split between absence of the transition below $d = 6$ and a nonperturbative fixed point that would permit it.","title":"Does a true Gardner transition exist in three-dimensional 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