Do offenses require intent?

In a mitzvah, there is a discussion about whether one fulfills one's duty or not. In offenses, there is no obligation, and therefore when there is no intention (meaning when he did not say, "For the sake of the uniqueness of God, I intend to transgress against His will"), it is not waived. It is true that I wrote that mitzvot require faith, and without faith, even offenses are not offenses. See my articles on the fall of a secular person into a transgression here on the site. Regarding "Do not add, not in eternity," there is a distinction between intending to add and not intending to.