  We present a first global closure test of the fixed parameterisation (MSHT)
approach to PDF fitting. We find that the default MSHT20 parameterisation can
reproduce the features of the input set in such a closure test to well within
the textbook uncertainties. This provides strong evidence that parameterisation
inflexibility in the MSHT20 fit is not a significant issue in the data region.
We also present the first completely like-for-like comparison between two
global PDF fits, namely MSHT and NNPDF, where the only difference is guaranteed
to be due to the fitting methodology. To achieve this, we present a fit to the
NNPDF4.0 data and theory inputs, but with the MSHT fixed parameterisation. We
find that this gives a moderately, but noticeably, better fit quality than the
central NNPDF4.0 fits, both with perturbative and fitted charm, and that this
difference persists at the level of the PDFs and benchmark cross sections. The
NNPDF4.0 uncertainties are found to be broadly in line with the MSHT results if
a textbook $T^2=1$ tolerance is applied, but to be significantly smaller if a
tolerance typical of the MSHT20 fit is applied. This points to an inherent
inconsistency between these approaches. We discuss the need for an enlarged
tolerance criterion in global PDF fits in detail, and demonstrate the impact of
data/theory inconsistencies in the closure test setting; namely, these do not
lead to any increase in the $T^2=1$ PDF uncertainty. We also investigate the
impact of restricting the PDF parameterisation to have fewer free parameters
than the default MSHT20 case, and find this can be significant at the level of
both closure tests and the full fit.
