A First Glimpse at the Shell Structure beyond ${}^{54}$Ca: Spectroscopy of ${}^{55}$K, ${}^{55}$Ca, and ${}^{57}$Ca

States in the $N=35$ and 37 isotopes ${}^{55,57}$Ca have been populated by direct proton-induced nucleon removal reactions from ${}^{56,58}$Sc and ${}^{56}$Ca beams at the RIBF. In addition, the $(p,2p)$ quasi-free single-proton removal reaction from ${}^{56}$Ca was studied. Excited states in ${}^{55}$K, ${}^{55}$Ca, and ${}^{57}$Ca were established for the first time via in-beam $\gamma$-ray spectroscopy. Results for the proton and neutron removal reactions from ${}^{56}$Ca to states in ${}^{55}$K and ${}^{55}$Ca for the level energies, excited state lifetimes, and exclusive cross sections agree well with state-of-the-art theoretical calculations using different approaches. The observation of a short-lived state in ${}^{57}$Ca suggests a transition in the calcium isotopic chain from single-particle dominated states at $N=35$ to collective excitations at $N=37$.