  A unique feature of generalised parton distributions is their relation to the
QCD energy-momentum tensor. In particular, they provide access to the
mechanical properties of the proton i.e. the distributions of pressure and
shear stress induced by its quark and gluon structure. In principle the
pressure distribution can be experimentally determined in a model-independent
way from a dispersive analysis of deeply virtual Compton scattering data
through the measurement of the subtraction constant. In practice the kinematic
coverage and accuracy of existing experimental data make this endeavour a
challenge. Elaborating on recent global fits of deeply virtual Compton
scattering measurements using artificial neural networks, our analysis presents
the current knowledge on this subtraction constant and assesses the impact of
the most frequent systematic assumptions made in this field of research. This
study will pave the way for future works when more precise data will become
available, e.g. obtained in the foreseen electron-ion colliders EIC and EIcC.
