  The moments of proton and net-proton multiplicity distributions are
observables expected to be sensitive to the QCD critical point and the nature
of the QCD phase transition from QGP to hadron gas. Hyper-order cumulants are
measured in wide centrality bins in STAR BES-I data and found to be
qualitatively consistent with trends predicted by lattice QCD which finds a
cross-over phase transition at low $\mu_\text{B}$. Data collected at
$\sqrt{s_{NN}}=3$ GeV in BES-II exhibit trends opposite of those observed in
higher energy collisions which may suggest the dominance of hadronic
interactions at this energy. The variance of proton multiplicity distributions
in azimuthal partitions is measured to search for signals of clustering
indicative of a first-order phase transition. A strong dependence on the event
multiplicity is observed. This dependence is independent of energy in AMPT
while in STAR data a significant trend with energy is observed.
