  We demonstrate the formation of gravitationally unstable discs in magnetized
molecular cloud cores with initial mass-to-flux ratios of 5 times the critical
value, effectively solving the magnetic braking catastrophe. We model the
gravitational collapse through to the formation of the stellar core, using
Ohmic resistivity, ambipolar diffusion and the Hall effect and using the
canonical cosmic ray ionization rate of $\zeta_\text{cr} = 10^{-17}$ s$^{-1}$.
When the magnetic field and rotation axis are initially aligned, a
$\lesssim1$~au disc forms after the first core phase, whereas when they are
anti-aligned, a gravitationally-unstable 25~au disc forms during the first core
phase. The aligned model launches a 3~km~s$^{-1}$ first core outflow, while the
anti-aligned model launches only a weak $\lesssim 0.3$~km~s$^{-1}$ first core
outflow. Qualitatively, we find that models with $\zeta_\text{cr} = 10^{-17}$
s$^{-1}$ are similar to purely hydrodynamical models if the rotation axis and
magnetic field are initially anti-aligned, whereas they are qualitatively
similar to ideal magnetohydrodynamical models if initially aligned.
