  The atomic masses of $^{55}$Sc, $^{56,58}$Ti, and $^{56-59}$V have been
determined using the high-precision multi-reflection time-of-flight technique.
The radioisotopes have been produced at RIKEN's RIBF facility and delivered to
the novel designed gas cell and multi-reflection system (ZD MRTOF), which has
been recently commissioned downstream of the ZeroDegree spectrometer following
the BigRIPS separator. For $^{56,58}$Ti and $^{56-59}$V the mass uncertainties
have been reduced down to the order of $10\,\mathrm{keV}$, shedding new light
on the $N=34$ shell effect in Ti and V isotopes by the first high-precision
mass measurements of the critical species $^{58}$Ti and $^{59}$V. With the new
precision achieved, we reveal the non-existence of the $N=34$ empirical
two-neutron shell gaps for Ti and V, and the enhanced energy gap above the
occupied $\nu p_{3/2}$ orbit is identified as a feature unique to Ca. We
perform new Monte Carlo shell model calculations including the $\nu d_{5/2}$
and $\nu g_{9/2}$ orbits and compare the results with conventional shell model
calculations, which exclude the $\nu g_{9/2}$ and the $\nu d_{5/2}$ orbits. The
comparison indicates that the shell gap reduction in Ti is related to a partial
occupation of the higher orbitals for the outer two valence neutrons at $N=34$.
