$Z=14$ Magicity Revealed by the Mass of the Proton Dripline Nucleus $^{22}$Si

Using the $B\rho$-defined isochronous mass spectrometry technique, we conducted the first mass measurement of the proton dripline nucleus $^{22}$Si. We confirm that $^{22}$Si is bound against particle emission with $S_p/S_{2p}=+1412(114)/+229(54)$ keV, fixing the proton dripline location for the Si element. By analyzing the mass differences of the neighboring $sd$-shell nuclei, we find that $^{22}$Si exhibits a doubly-magic character similar to its mirror partner $^{22}$O, and that the mirror energy difference of $^{22}$Si-$^{22}$O deviates from the predictions assuming mirror symmetry. Gamow shell-model calculations reveal that the average occupations of valence protons in $^{22}$Si are nearly identical to those of valence neutrons in $^{22}$O, supporting the $Z=14$ magicity in $^{22}$Si. The observed mirror-symmetry breaking is attributed to the extended proton distribution in $^{22}$Si arising from a small contribution of the unbound $\pi2s_{1/2}$ orbital.