  We study universal off-diagonal correlations in transverse quantum fluids
(TQF) -- a new class of quasi-one-dimensional superfluids featuring
long-range-ordered ground states. These exhibit unique self-similar space-time
relations scaling with $x^2/D\tau$ that serve as fingerprints of the specific
states. The results obtained with the effective field theory are found to be in
perfect agreement with {\it ab initio} simulations of hard-core bosons on a
lattice -- a simple microscopic realization of TQF. This allows an accurate
determination -- at nonzero temperature and finite system size -- of such key
ground-state properties as the condensate and superfluid densities, and
characteristic parameter $D$.
