This is the 3345th most frequent Japanese word.
断じて
Absolutely; positively; resolutely.
The word 『断じて』 is used here to express an emphatic negation, indicating absolute certainty that the statement is not true.
これは断じて間違いではありません。
This is absolutely not a mistake.
In this context, 『断じて』 functions to strongly deny the allegation of lying, reinforcing the veracity of her honesty.
彼女は断じて嘘をつきませんでした。
She absolutely did not lie.
Here, 『断じて』 conveys a firm stance or unyielding decision about not forgiving.