  The black-hole binary system LMC X-3 has been observed by virtually every
X-ray mission since the inception of X-ray astronomy. Among the persistent
sources, LMC X-3 is uniquely both habitually soft and highly variable. Using a
fully relativistic accretion-disk model, we analyze hundreds of spectra
collected during eight X-ray missions that span 26 years. For a selected sample
of 391 RXTE spectra we find that to within ~2 percent the inner radius of the
accretion disk is constant over time and unaffected by source variability. Even
considering an ensemble of eight X-ray missions, we find consistent values of
the radius to within ~4-6 percent. Our results provide strong evidence for the
existence of a fixed inner-disk radius. The only reasonable inference is that
this radius is closely associated with the general relativistic innermost
stable circular orbit (ISCO). Our findings establish a firm foundation for the
measurement of black hole spin.
