  We present the first estimate of the intrinsic binary fraction of young stars
across the central $\approx$ 0.4 pc surrounding the supermassive black hole
(SMBH) at the Milky Way Galactic center (GC). This experiment searched for
photometric variability in 102 young stars, using 119 nights of 10"-wide
adaptive optics imaging observations taken at Keck Observatory over 16 years in
the K'- and H-bands. We photometrically detected three binary stars, all of
which are situated more than 1" (0.04 pc) from the SMBH and one of which,
S2-36, is newly reported here with spectroscopic confirmation. To convert the
observed binary fraction into an estimate of the underlying binary fraction, we
determined experiment sensitivity through detailed light curve simulations,
incorporating photometric effects of eclipses, irradiation, and tidal
distortion in binaries. The simulations assumed a population of young binaries,
with stellar ages (4 Myr) and masses matched to the most probable values
measured for the GC young star population and underlying binary system
parameters similar to those of local massive stars. The detections and
simulations imply young, massive stars in the GC have a stellar binary fraction
$\geq$ 71% (68% confidence), or $\geq$ 42% (95% confidence). This inferred GC
young star binary fraction is consistent with that typically seen in young
stellar populations in the solar neighborhood. Furthermore, our measured binary
fraction is significantly higher than that recently reported by Chu et al.
(2023) based on RV measurements of young stars <~1" of the SMBH. Constrained
with these two studies, the probability that the same underlying young binary
fraction extends across the entire region is <1.4%. This tension provides
support for a radial dependence of the binary star fraction and, therefore, for
the dynamical predictions of binary merger and evaporation events close to the
SMBH.
