  We address the turbulent fragmentation scenario for the origin of the stellar
initial mass function (IMF), using a large set of numerical simulations of
randomly driven supersonic MHD turbulence. The turbulent fragmentation model
successfully predicts the main features of the observed stellar IMF assuming an
isothermal equation of state without any stellar feedback. As a test of the
model, we focus on the case of a magnetized isothermal gas, neglecting stellar
feedback, while pursuing a large dynamic range in both space and timescales
covering the full spectrum of stellar masses from brown dwarfs to massive
stars. Our simulations represent a generic 4 pc region within a typical
Galactic molecular cloud, with a mass of 3000 Msun and an rms velocity 10 times
the isothermal sound speed and 5 times the average Alfven velocity, in
agreement with observations. We achieve a maximum resolution of 50 au and a
maximum duration of star formation of 4.0 Myr, forming up to a thousand sink
particles whose mass distribution closely matches the observed stellar IMF. A
large set of medium-size simulations is used to test the sink particle
algorithm, while larger simulations are used to test the numerical convergence
of the IMF and the dependence of the IMF turnover on physical parameters
predicted by the turbulent fragmentation model. We find a clear trend toward
numerical convergence and strong support for the model predictions, including
the initial time evolution of the IMF. We conclude that the physics of
isothermal MHD turbulence is sufficient to explain the origin of the IMF.
