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We report the discovery of three binary millisecond pulsars during the Parkes Multibeam Pulsar Survey of the Galactic Plane. The objects are highly recycled and are in orbits of many tens of days about low-mass white-dwarf companions. The eccentricity of one object, PSR J1853+1303, is more than an order of magnitude lower than predicted by the theory of convective fluctuations during tidal circularization. We demonstrate that, under the assumption that the systems are randomly oriented, current theoretical models of the core-mass--orbital-period relation for the progenitors of these systems likely overestimate the white-dwarf masses, strengthening previous concerns about the match of these models to the data. The new objects allow us to update the limits on violation of relativistic equivalence principles to 95% confidence upper limits of 5. 5 x 10^-3 for the Strong Equivalence Principle parameter Delta and 4. 0 x 10^-20 for the Lorentz-invariance/momentum-conservation parameter alpha₃.
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