Does a new marriage after a minor irrevocable divorce (baynunah sughra) invalidate the previous revocable divorces? Is the second marriage contract recorded in a separate document? And is a divorce after the second marriage considered a first revocable divorce or a completion of the three?

If a man divorces his wife with a minor irrevocable divorce, such as through Khul' (divorce at the wife's instance) or a revocable divorce whose 'iddah (waiting period) has expired, and he wishes to take her back, then a new marriage contract (nikah) that fulfills all its pillars (wali/guardian, two just witnesses, mahr/dowry, and صيغة/ صيغة الإيجاب والقبول / explicit offer and acceptance) is necessary. The husband still retains two divorces from the wife's 'ismah (marital bond), because the 'ismah does not end except with three divorces, as indicated by the Almighty's saying: "Divorce is twice. Then, either keep [her] in kindness or release [her] with good treatment." Therefore, the new contract after a minor irrevocable divorce does not invalidate the previous divorce nor does it change what remains of the 'ismah. The marriage contract becomes valid upon the fulfillment of its pillars, and its validity does not depend on registration in a document. Registering the second contract is a matter of expediency, and a divorce that occurs after the second contract is considered a completion of the three if it was preceded by two divorces.