  We demonstrate that the zero-temperature superconducting phase diagram of
underdoped cuprates can be quantitatively understood in the strong binding
limit, using only the experimental spectral function of the "normal" pseudo-gap
phase without any free parameter. In the prototypical
(La$_{1-x}$Sr$_x$)$_2$CuO$_4$, a kinetics-driven $d$-wave superconductivity is
obtained above the critical doping $\delta_c\sim 5.2\%$, below which complete
loss of superfluidity results from local quantum fluctuation involving local
$p$-wave pairs. Near the critical doping, a enormous mass enhancement of the
local pairs is found responsible for the observed rapid decrease of phase
stiffness. Finally, a striking mass divergence is predicted at $\delta_c$ that
dictates the occurrence of the observed quantum critical point and the abrupt
suppression of the Nernst effects in the nearby region.
