  We study the leading-power gluon transverse momentum dependent distributions
(TMDs) of relevance to the study of asymmetries in the scattering off
transversely polarized hadrons. Next-to-leading-order perturbative calculations
of these TMDs show that at large transverse momentum they have common dynamical
origins, but that in the limit of small longitudinal momentum fraction $x$ only
one origin remains. We find that in this limit only the dipole-type gluon TMDs
survive and become identical to each other. At small $x$ they are all given by
the expectation value of a single Wilson loop inside the transversely polarized
hadron, the so-called spin-dependent odderon. This universal origin of
transverse spin asymmetries at small $x$ is of importance to current and future
experimental studies, paving the way to a better understanding of the role of
gluons in the three-dimensional structure of spin-polarized protons.
