At the risk of excessive red tape, the judicial system has been doing a reasonable job of determining facts in most modern countries.

It actually doesn't. Example: Did OJ kill anybody?

Judicial system engages in determining whether someone is guilty based on the evidence that it itself filters.

What about more complex things? Like what if I say "P = NP"? Is that a lie?

And then, do you want a trial for every comment? That will not work even for a fraction of comments.

>Like what if I say "P = NP"? Is that a lie?

That can't be determined to be a lie unless someone solves the problem. It's only a conjecture or assertion until then.

>And then, do you want a trial for every comment? That will not work even for a fraction of comments.

Only really has to apply to political statements made by the most powerful office holders, and only when contested, and only when there is a imminent intent to deceive and impact policy.

It's not really an all-or-nothing situation. It's just a matter of how much can be achieved within a reasonable cost.