The Ariadne Incident is a space-time anomaly that was produced as a result of the Zohar Emulators going out of control, when the U-TIC Organization was running connection experiments with the emulators at a facility located on the planet Ariadne. Ariadne completely disappeared within the anomaly, along with with its 1.5 billion inhabitants. However, there were a few spaceships that had managed to escape. These included ships owned by the U-TIC Organization.
According to the database in Xenosaga Episode III: Also sprach Zarathustra, a connection, a Zohar Link Experiment, was made to the link experiment's director Andrew Cherenkov and the reason behind Ariadne being the location for the connection experiments. It was on Ariadne that Cherenkov was in a sham marriage, and committed murder repeatedly, and he had been placed in a personality reconditioning facility. This could be why he chose Ariadne to be the place for his martyrdom.