The anti-time past was an alternate version of 2364 created as the result of a paradox involving an anti-time eruption formed in the Devron system in an unknown future year.

In this timeline, Jean-Luc Picard disobeyed Starfleet orders virtually from the moment he arrived on board the USS Enterprise-D at Earth Station McKinley. He subsequently called a red alert while docked at the station, ordered the ship to the Devron system instead of to Farpoint Station and took the vessel into the temporal anomaly. Within the anomaly, the Enterprise-D met with the two historically-later versions of itself and created a static warp shell to seal the eruption, after which this timeline and the anti-time future ceased to exist. (TNG: "All Good Things...")

Anti-time eruption timelines
Past • Present • Future