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Current descriptions of the pseudogap in underdoped cuprates envision adoping-dependent transition line $T^*(p)$ which descends monotonically towardszero just beyond optimal doping. There is much debate as to the location of theterminal point $p^*$ where $T^*(p)$ vanishes, whether or not there is a phasetransition at $T^*$ and exactly how $T^*(p)$ behaves below $T_c$ within thesuperconducting dome. One perspective sees $T^*(p)$ cutting the dome andcontinuing to descend monotonically to zero at $p_{crit} \approx 0.19$ holes/Cu$-$ referred to here as `entrant behavior'. Another perspective derived fromphotoemission studies is that $T^*(p)$ intersects the dome near $p_{crit}\approx 0.23$ holes/Cu then turns back below $T_c$, falling to zero againaround $p_{crit} \approx 0.19$ $-$ referred to here as `reentrant behavior'. Byexamining thermodynamic data for Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ we showthat neither entrant nor reentrant behavior is experimentally supported.Rather, $p_{crit} \approx 0.19$ sharply delimits the pseudogap regime and for$p < 0.19$ the pseudogap is always present, independent of temperature. Similarresults are found for Y$_{0.8}$Ca$_{0.2}$Ba$_2$Cu$_3$O$_{7-\delta}$. For bothmaterials $T^*(p)$ is not a temperature but a crossover scale, $\approxE^*(p)/2k_B$, reflecting instead the underlying pseudogap energy $E^*(p)$ whichvanishes as $p \rightarrow 0.19$.

Locating the pseudogap closing point in cuprate superconductors: absence of entrant or reentrant behavior