  In so-called $j_\mathrm{eff} = 1/2$ systems, including some iridates and
ruthenates, the coherent superposition of $t_\mathrm{2g}$ orbitals in the
ground state gives rise to hopping processes that strongly depend on the bond
geometry. Resonant inelastic x-ray scattering (RIXS) measurements on CaIrO$_3$
reveal a prototypical $j_\mathrm{eff} = 1/2$ pseudospinon continuum, a hallmark
of one-dimensional (1D) magnetic systems despite its three-dimensional crystal
structure. The experimental spectra compare very well to the calculated
magnetic dynamical structure factor of weakly coupled spin-1/2 chains. We
attribute the onset of such quasi-1D magnetism to the fundamental difference in
the magnetic interactions between the $j_\mathrm{eff} = 1/2$ pseudospins along
the corner- and edge-sharing bonds in CaIrO$_3$.
