A solitary millisecond pulsar, if near the mass limit, and undergoing
a phase transition, either first or second order, provided the transit
ion is to a substantially more compressible phase, will emit a blatant
ly obvious signal-spontaneous spin-up, Normally a pulsar spins down by
angular momentum loss to radiation. The signal is trivial to detect a
nd is estimated to be ''on'' for 1/50 of the spin-down era of millisec
ond pulsars. Presently about 25 solitary millisecond pulsars are known
. The phenomenon is analogous to ''backbending'' observed in high spin
nuclei in the 1970's.