[AdamJacobMuller]

My understanding is that, no, the government cannot compel you to speak falsely or, generally, to do other things you don't want to do.

As I understand it, this is related to the argument that Apple was using vs the FBI recently, that while the FBI could compel Apple to produce things in its possession (like Farook's iCloud backups) it could not compel Apple to do things like produce a custom version of iOS.

IANAL, but, this is mostly based on what I remember reading last year when the whole warrant canary idea first started getting publicized.