Debian
The Pyra will, as shipped, run Debian, using the official Debian ARMhf repo for most software, with hardware-specific packages available from a repo on pyra-handheld.com.
Images and Installer at http://packages.pyra-handheld.com/images/
List of software in Debian at https://packages.debian.org/jessie/ (check for armhf as the architecture)