Does divorce take effect merely by the husband's utterance of the word "punishment," given that the wife lied, and is she obligated to ask him about his intention?

Lying is a grave sin, and regretting it is a good repentance if its conditions are met. Do not excessively search for your husband's intention regarding the punishment he did not specify, so that you do not fall into embarrassment and whispers [of doubt]. Spouses should avoid problems, be patient, and maintain good companionship as much as possible.