  The hidden order in URu$_2$Si$_2$ remains a compelling mystery after more
than thirty years, with the order parameter still unidentified. One intriguing
proposal for the phase has been hastatic order: a symmetry breaking heavy Fermi
liquid with a spinorial hybridization that breaks both single and double
time-reversal symmetry. Hastatic order is the first spinorial, rather than
vectorial order in materials, but previous work has not yet found direct
consequences of the spinorial nature. In this paper, we revisit the hastatic
proposal within Landau-Ginzburg theory. Rather than a single spinorial order
parameter breaking double-time-reversal symmetry, we find two gauge invariant
vectorial orders: the expected composite order with on-site moments, and a new
quantity capturing symmetries broken solely by the spinorial nature. We address
the effect of fluctuations and disorder on the tetragonal symmetry breaking,
explaining the absence of in-plane moments in URu$_2$Si$_2$ and predicting a
new transition in transverse field.
