A model for high-temperature superconductors incorporating antiferromagnetism, d-wave superconductivity, and no double latticesite occupancy can give energy surfaces delicately 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 to separate essential from peripheral in the superconducting mechanism.high-temperature superconductivity, pseudogap, critical dynamical symmetry, inhomogeneity, complexity, emergent behavior High-temperature superconductivity was discovered more than two decades ago [1], but its interpretation remains controversial [2,3]. We believe that this lack of theoretical consensus may be attributed to two fundamental, and related, issues: (1) Most models emphasize a limited aspect of the (complex) problem; as a result, there are few solvable models that capture a sufficient range of essential physics. (2) The complex behavior of these compounds obscures the superconducting mechanism because, in the absence of solvable models incorporating a sufficiently wide range of the physics, it is difficult to separate essential from secondary features using only data. For example, high-temperature superconductors exhibit a variety of spatial inhomogeneities such as stripes or checkerboards, particularly in the hole-underdoped region and near magnetic vortex cores [4][5][6][7][8]. The relationship of these inhomogeneities to the unusual properties of these systems has yet to be settled. Does it lead to superconductivity (SC)?