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We describe the relation between spin fluctuations and superconductivity in a highly ordered sample of ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6.5}$ using both polarized and unpolarized neutron inelastic scattering. The spin susceptibility in the superconducting phase exhibits one-dimensional incommensurate modulations at low energies, consistent with hydrodynamic stripes. With increasing energy the susceptibility curves upward to …