  A model for high-temperature superconductors incorporating
antiferromagnetism, d-wave superconductivity, and no double lattice-site
occupancy can give energy surfaces exquisitely balanced between
antiferromagnetic and superconducting order for specific ranges of doping and
temperature. The resulting properties can reconcile a universal cuprate phase
diagram with rich inhomogeneity, relate that inhomogeneity to pseudogaps, give
a fundamental rationale for giant proximity effects and other emergent
behavior, and provide an objective framework for separating essential from
peripheral in the superconducting mechanism.
