How many 3440 x 1440 monitors can you connect to the latest MacPro?

Apple is not clean in:

Mac Pro (Late 2013): Using multiple displays - Apple Support

It includes

Can I connect more than 2 DVI or HDMI displays?

Mac Pro supports a total of two DVI or HDMI displays when connected via the built-in HDMI port or using the Apple Mini DisplayPort to DVI adapter. To connect additional DVI displays, use an active DVI adaptersuch as the Apple Mini DisplayPort to Dual-Link DVI adapter. You can connect up to six active adapter DVI displays. This requires a powered USB hub since Mac Pro offers four USB ports and you will need six to connect them all.

However, that article says:

Six Apple Thunderbolt Displays (27-inch), Apple LED Cinema Displays (27-inch), or third-party Mini DisplayPort displays.

So it appears you can with active dual-link DVI adopter or monitors with a display/min displayport connection.

The Apple LED Cinema Displays (27-inch) and Thunderbolt display is 2560 × 1440 but yours is 3440 x 1440. Thus it is unclear how many you count run