  What are the most important conditions and processes governing the growth of
stellar-origin compact objects? The identification of compact object type as
either black hole (BH) or neutron star (NS) is fundamental to understanding
their formation and evolution. To date, time-domain determination of compact
object type remains a relatively untapped tool. Measurement of orbital periods,
pulsations, and bursts will lead to a revolution in the study of the
demographics of NS and BH populations, linking source phenomena to accretion
and galaxy parameters (e.g., star formation, metallicity). To perform these
measurements over sufficient parameter space, a combination of a wide-field
(>5000 deg^2) transient X-ray monitor over a dynamic energy range (~1-100 keV)
and an X-ray telescope for deep surveys with <5 arcsec PSF half-energy width
(HEW) angular resolution are required. Synergy with multiwavelength data for
characterizing the underlying stellar population will transform our
understanding of the time domain properties of transient sources, helping to
explain details of supernova explosions and gravitational wave event rates.
