Learn Spanish (Latin America): No afirmamos categóricamente que la calumnia sea cierta. - We do not categorically state that the slander is true.

The phrase No afirmamos que (We do not state that) is a negative communication trigger. While affirmative statements like Afirmamos que declare a fact and use the indicative, negating the communication verb introduces doubt or denies the statement, requiring the subjunctive sea.

Would the sentence still use the subjunctive if we removed the word No?

No. If the sentence were affirmative (Afirmamos categóricamente que...), you would use the indicative es. Affirmative communication verbs declare information as a fact, while their negative counterparts deny or question it, triggering the subjunctive.

Why do we use a form of ser (sea) instead of estar with cierta?

In Spanish, being true or false is treated as an inherent defining characteristic of a statement, not a temporary state. Therefore, you always use ser with cierto or cierta.

Can I place categóricamente somewhere else in the sentence?

Yes, though its current position immediately after the verb afirmamos is the most natural. You could place it at the very beginning for strong emphasis, but putting it after the verb smoothly modifies how the stating is done without disrupting the connection to the que clause.