Earlier quoted context omitted.
> acting negligently > knew that it was false Wrong. The bar for negligence is "should have performed X, but failed to do so". Ex: A toddler dying by falling off a deck is negligence. The homeowner "should have repaired the deck", but failed to do so. (This bar would lead to negligent homicide or manslaughter, depending on jurisdiction). Similarly, a journalist "should have done basic research", but failed to do so,…
The standard relevant in most defamation cases is recklessness, not negligence.
But LII at least suggests that the law as written, is about negligence: https://www.law.cornell.edu/wex/defamation
EDIT: According to LII on libel: https://www.law.cornell.edu/wex/libel, there seems to be different awards for negligence, recklessness, and malice. Negligence is capped at actual injury, while recklessness and above can have punitive damages.
EDIT: Alex Jones's $965M penalty here is likely punitive? (I don't know for sure), which suggests that it was at least of the reckless level and proven so in court?