  The stellar initial mass function (IMF) is an underlying distribution
function which determines many important observables, from the number of
ionizing photons in a population of some age and metallicity, through the
creation rate of various chemical elements, to the mass to light ratio of a
system. This significance, together with the empirical difficulty to determine
the IMF robustly, and the near complete lack of any robust theoretical
predictor, has allowed investigators freedom to treat the IMF as a continuously
variable parameterisation of astrophysicists' ignorance of complexity. An
ability to vary a parameter in a model is not the same as a true variation in a
physical system. A more instructive approach is to use available data to
constrain possible variations, and thereby to allow identification of those
other aspects of an observed system whose understanding can be improved.
Ideally, the most sensitive physical variable, or its parameterisation, should
be the best constrained. A fundamental null hypothesis, which we defend here,
is that the IMF is a universal invariant function, so that all apparent
variations may be ascribed to other variables, and to irreducible statistical
sampling fluctuations.
