  A contact interaction is used to calculate an array of pion twist-two, -three
and -four generalised transverse light-front momentum dependent parton
distribution functions (GTMDs). Despite the interaction's simplicity, many of
the results are physically relevant, amongst them a statement that GTMD size
and shape are largely prescribed by the scale of emergent hadronic mass.
Moreover, proceeding from GTMDs to generalised parton distributions (GPDs), it
is found that the pion's mass distribution form factor is harder than its
electromagnetic form factor, which is harder than the gravitational pressure
distribution form factor; the pressure in the neighbourhood of the pion's core
is commensurate with that at the centre of a neutron star; the shear pressure
is maximal when confinement forces become dominant within the pion; and the
spatial distribution of transversely polarised quarks within the pion is
asymmetric. Regarding transverse momentum dependent distribution functions
(TMDs), their magnitude and domain of support decrease with increasing twist.
The simplest Wigner distribution associated with the pion's twist-two
dressed-quark GTMD is sharply peaked on the kinematic domain associated with
valence-quark dominance; has a domain of negative support; and broadens as the
transverse position variable increases in magnitude.
