Somewhere between the known and the unknowable, physicists have long suspected that matter harbors configurations stranger than the textbooks allow. Three such configurations—exotic five-quark particles called pentaquarks—are now the subject of a proposal to study them through electron-positron collisions at a next-generation facility called the Super Tau-Charm Facility, where the sheer intensity of collisions could finally yield enough data to settle deep questions about their inner nature. The work is less a discovery than a map drawn in advance of the journey: a careful calculation of what