  Recent research has demonstrated the existence of a new type of solar event,
the "terminator." Unlike the Sun's signature events, flares and Coronal Mass
Ejections, the terminator most likely originates in the solar interior, at or
near the tachocline. The terminator signals the end of a magnetic activity
cycle at the Sun's equator and the start of a sunspot cycle at mid latitudes.
Observations indicate that the time difference between these events is very
short, less than a solar rotation, in the context of the sunspot cycle. As the
(definitive) start and end point of solar activity cycles the precise timing of
terminators should permit new investigations into the meteorology of our star's
atmosphere. In this letter we use a standard method in signal processing, the
Hilbert transform, to identify a mathematically robust signature of terminators
in sunspot records and in radiative proxies. Using a linear extrapolation of
the Hilbert phase of the sunspot number and F10.7 solar radio flux time series
we can achieve higher fidelity historical terminator timing than previous
estimates have permitted. Further, this method presents a unique opportunity to
project, from analysis of sunspot data, when the next terminator will occur,
May 2020 ($+4$, $-1.5$ months), and trigger the growth of sunspot cycle 25.
