How are the Official Ubuntu Vagrant boxes built and published to Atlas?

You would be correct that the build process for Ubuntu images is all open!

For 16.04 and newer

Look at the livecd-rootfs package for how the images are built:

• https://code.launchpad.net/~ubuntu-core-dev/livecd-rootfs/trunk
• http://bazaar.launchpad.net/~ubuntu-core-dev/livecd-rootfs/trunk/view/head:/live-build/ubuntu-cpc/hooks/042-vagrant.binary

For older releases of Ubuntu

• https://code.launchpad.net/~ubuntu-on-ec2
• https://launchpad.net/vmbuilder

Specifically:

• https://code.launchpad.net/~ubuntu-on-ec2/vmbuilder/jenkins_kvm

And this is probably what you're looking for:

• http://bazaar.launchpad.net/~ubuntu-on-ec2/vmbuilder/jenkins_kvm/view/head:/jenkins/CloudImages_Vagrant.sh