  We investigate the universal thermodynamics of the two-component
one-dimensional Bose gas with contact interactions in the vicinity of the
quantum critical point separating the vacuum and the ferromagnetic liquid
regime. We find that the quantum critical region belongs to the universality
class of the spin-degenerate impenetrable particle gas which, surprisingly, is
very different from the single-component case and identify its boundaries with
the peaks of the specific heat. In addition, we show that the compressibility
Wilson ratio, which quantifies the relative strength of thermal and quantum
fluctuations, serves as a good discriminator of the quantum regimes near the
quantum critical point. Remarkably, in the Tonks-Girardeau regime the universal
contact develops a pronounced minimum, reflected in a counterintuitive
narrowing of the momentum distribution as we increase the temperature. This
momentum reconstruction, also present at low and intermediate momenta, signals
the transition from the ferromagnetic to the spin-incoherent Luttinger liquid
phase and can be detected in current experiments with ultracold atomic gases in
optical lattices.
