Commentaire sur Le Lévitique 5:4

בשפתים [OR IF A SOUL SWEAR, PRONOUNCING] WITH HIS LIPS [FOR HARM, OR FOR GOOD] — with his lips but not merely in his heart (Sifra, Vayikra Dibbura d'Chovah, Section 9 2; Shevuot 26b).

But not with his heart. I.e., if he decided in his heart by making an oath silently without verbalizing not to eat, and then he ate, he is not liable to bring an offering.

לאחת מאלה, “be guilty concerning one of these things.” Concerning this Rashi asks what the Torah means to tell us with these words? (Actually on verse 13, where the same expression occurs, not on this verse) he answers that the three different sins all involving oaths that are being mentioned here are being treated equally. He answers that I could have thought that the type of offering demanded would be determined by the relative severity of the sin, whereas theTorah reveals that it is determined by the economic status of the sinner concerned. For example: if the person concerned had by mistake eaten part of an offering, he basically has to atone for this by offering a sheep or female goat. If he had committed a less serious sin, by failing to testify to something he had been a witness of, he has to bring a bird offering. If his inadvertent sin consisted of swearing an oath concerning what he would or would not do, and had forgotten that he had expressed this by words that made it an oath, he will bring a meal offering as atonement consisting of about two kilos of flour.