The conversion of nuclear matter to quark matter in the core of a rotating neutron star alters its moment of inertia. Hence the epoch over which conversion takes place will be signaled in the spin-down "signal_prl.tex" 581 lines, 22203 characters characteristics of pulsars. We find that an observable called the braking index should be easily measurable during the transition epoch and can have a value far removed (by orders of magnitude) from the canonical value of three expected for magnetic

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... ole radiation, and may have either sign. The duration of the transition epoch is governed by the slow loss of angular momentum to radiation and is further prolonged by the reduction in the moment of inertia caused by the phase change which can even introduce an era of spin-up. We estimate that about one in a hundred pulsars may be passing through this phase. The phenomenon is analogous to "bachbending" observed in the moment of inertia of rotating nuclei observed in the 1970's, which also signaled a change in internal structure with changing spin.