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A nonlinear complex scalar field theory with a global phase symmetry and a curved target-space kinetic coefficient. In physical coordinates its classical density is displayed above; dimensionless coordinates measured in $M^{-1}$ put a common $M^2$ outside the reduced density. Its regular coordinate domain is ${\lambda }^2|\psi {|}^2<1$. Rotating localized solutions are charged complex sine-Gordon solitons. The local classical density does not by itself specify the treatment of the singular coordinate boundary or a global quantum completion.