  A simple dynamical model, Biased Random Organization, BRO, appears to produce
configurations known as Random Close Packing (RCP) as BRO's densest critical
point in dimension $d=3$. We conjecture that BRO likewise produces RCP in any
dimension; if so, then RCP does not exist in $d=1-2$ (where BRO dynamics lead
to crystalline order). In $d=3-5$, BRO produces isostatic configurations and
previously estimated RCP volume fractions 0.64, 0.46, and 0.30, respectively.
For all investigated dimensions ($d=2-5$), we find that BRO belongs to the
Manna universality class of dynamical phase transitions by measuring critical
exponents associated with the steady-state activity and the long-range density
fluctuations. Additionally, BRO's distribution of near-contacts (gaps) displays
behavior consistent with the infinite-dimensional theoretical treatment of RCP
when $d \ge 4$. The association of BRO's densest critical configurations with
Random Close Packing implies that RCP's upper-critical dimension is consistent
with the Manna class $d_{uc} = 4$.
