Exactly. Seeing as there is no presumption of innocence in the US and the burden of proof is the defendant’s, it makes sense that a judge can put anyone in jail indefinitely without proving anything. If he had died in prison it would have been due process because contempt is meant to be so punitive that it acts as a deterrent to any other person that sets foot in a court room from refusing to be compelled into making self-incriminatory statements.

Now obviously this entire line of reasoning would be completely nullified if there were examples to the contrary or if any of the things mentioned had been adjudicated before but