From arguments in US v. Alvarez:

JUSTICE ALITO: Do you really think that there is — that the First Amendment — that there is First Amendment value in a bald-faced lie about a purely factual statement that a person makes about himself, because that person would like to create a particular persona? Gee, I won the Medal of Honor. I was a Rhodes scholar, I won the Nobel Prize. There’s a personal -­ the First Amendment protects that?

MR. LIBBY: Yes, Your Honor, so long as it doesn’t cause imminent harm to another person or imminent harm to a government function.

JUSTICE BREYER: Obvious example. Are there Jews hiding in the cellar? No.

MR. LIBBY: Well, that’s right.

CHIEF JUSTICE ROBERTS: That’s not a statement about one’s self. This is -­

MR. LIBBY: And that’s -­
JUSTICE BREYER: Are you hiding Jews in the  cellar?

CHIEF JUSTICE ROBERTS: Excuse me. Sorry. (Laughter.)

And this RBG bomb about holocaust denial:

JUSTICE GINSBURG: Well, the assumption -­ 5 the assumption is that it’s false, that was — and that 6 it’s not so hard to find out if somebody claimed to have 7 the Medal of Honor and he doesn’t. So that — first you 8 answered yes, that it’s only self, and now you said, no, 9 it can be — or at least I think you said — making a 10 false statement of fact. And the concern is — and I 11 gave you the question of just in the service, leaving 12 out the decorations — other statements of fact, false 13 statements like “I deny that the Holocaust ever 14 occurred.” That’s a statement, a false statement of 15 fact, isn’t it?

GENERAL VERRILLI: Yes, it could be. I 17 think a statute seeking to regulate that, Justice 18 Ginsburg, would have viewpoint discrimination problems 19 of the kind that the Court identified in R.A.V., and I 20 think also under the Court’s “breathing space” analysis 21 you would — you’d have to look long and hard and have 22 significant concerns about that kind of a — a 23 statement, because it’s so bound up with matters of 24 ideological controversy that — that you’d want to 25 exercise care, but that’s really quite different from 1 what we have here. 2 This is a pinpoint accuracy, a specific 3 verifiable factual claim about yourself having won a 4 medal.