Singularity is now back online with the new mirror and the new build, which includes multiple characters in training.  There is an important known issue that is detailed below.

The EVE launcher will try to start the client with DX11, which will result in a black screen.  To fix this, go to the settings in the launcher (small cog-wheel in the top right corner), switch to the tab "DirectX" and select dx9. Then start the client as usual.  Any issues you have with this can be reported in the following thread: https://forums.eveonline.com/default.aspx?g=posts&t=287760&find=unread