  We find evidence that for zero spin density $m=0$, intermediate $U/4t$
values, and a range $x\in (x_c,x_*)$ of finite hole concentrations the ground
state of the virtual-electron pair quantum liquid obtained from perturbing the
square-lattice quantum liquid of Ref. \cite{companion2} by weak
three-dimensional (3D) uniaxial anisotropy and intrinsic disorder has
long-range d-wave superconducting order. Here $t$ is the effective
nearest-neighbor transfer integral and $U$ the effective on-site repulsion. The
long-range d-wave superconducting order emerges below a critical temperature
$T_c$ for a hole concentration range centered at $x_{op}= (x_c+x_*)/2$. It
results from the effects of the residual interactions of the charge $c$
fermions and spin-neutral two-spinon $s1$ fermions of Ref. \cite{companion2},
as a by-product of the short-range spin correlations. Rather than the U(1)
symmetry contained in the $\eta$-spin SU(2) symmetry of the $SO(4) =
[SU(2)\times SU(2)]/Z_2$ symmetry, the U(1) symmetry broken at $T_c$ is the $c$
fermion U(1) symmetry of Ref. \cite{bipartite}. It is contained in the extended
global $SO(3)\times SO(3)\times U(1)=[SO(4)\times U(1)]/Z_2$ symmetry of the
Hubbard model on the square lattice. Our preliminary results seem to indicate
that combining the electronic correlations described by the square-lattice
quantum liquid perturbed by 3D uniaxial anisotropy with the very weak effects
of intrinsic disorder or superfluid-density anisotropy leads for the
hole-concentration range $x\in (x_c,x_*)$ to a successful description of the
universal properties of the hole-doped cuprate superconductors.
