It isn't. That would be de-jure truth. My assumption is based on the fact that with my internal states of knowledge it is an obvious deduction (not inference, mind, this is mathematics). I also have some nice conversational arguments for it.

So you are personally persuaded of it, and have unstated arguments for it.

Also, the "proof" of the Tegmark 4 hypothesis tastes like it might run into some Gödelian complications.

Another remark which is much less interesting than production of the proof itself.

Other things I would call de-facto

These are things I would call "punting", or personally comitting to.