Can the government compel you to lie?

Inspired by this thread.

In the United States, is it possible for Law…at some level, be it federal, state, county, or municipal…make a citizen, under penalty (fines, arrest, imprisonment) to not simply believe but profess a falsity?

Compel you to make a statement contrary to evidence or conscience?

Some government agents lie regularly as part of their job description. Policemen working undercover, or while interrogating a suspect. Intelligence agents spread false information to the enemy. If they suddenly develop an opposition to falsehood, then at minimum they would lose their jobs.

I suppose this might be required to some degree for state secrets/national security info. Like, a CIA agent being required to maintain cover and never reveal certain information. I would imagine that some kinds of information can only really be protected by intelligence officials telling lies to supply a false narrative. But I can’t think of any other kind of example.

Some people given new identities may be compelled to lie as a condition of the new identity.

Plea bargaining.

I am not a lawyer, but in cases of testimony or official statements, I don’t believe so based on the 5th Amendment, and the premise of Entrapment.. On the one hand, the US government cannot compel you to testify against yourself, and on the other hand, if you are not predisposed to lying about a fact, then the government skates on liquid ice to compel you to do so.

On the other hand, I routinely use the “No comment,” or “I can neither confirm nor deny” statements at work. It’s not a lie, it’s just a lack of acknowledgement.

I plead the 5th.

What about warrant canaries? Commenting on an Australian law outlawing them, Bruce Schneier said

So, the question would be, could the U.S. government compel a private citizen–or a private organization–to (falsely) say “Gosh, no, Mr. Customer, we weren’t served with a warrant/FISA warrant/national security letter compelling us to turn over your information”?