  The universal Tan relations connect a variety of microscopic features of
many-body quantum systems with two-body contact interactions to a single
quantity, called the contact. The latter has become pivotal in the description
of quantum gases.We provide a complete characterization of the Tan contact of
the harmonically trapped Lieb-Liniger gas for arbitrary interactions and
temperature.Combining thermal Bethe ansatz, local-density approximation, and
exact quantum Monte Carlo calculations,we show that the contact is a universal
function of only two scaling parameters, and determine the scaling function.We
find that the temperature dependence of the contact, or equivalently the
interaction dependence of the entropy, displays a maximum. The presence of this
maximum provides an unequivocal signature of the crossover to the fermionized
regime and it is accessible in current experiments.
