As of this morning, according to CNN and Fox, Israel sent conditions to the Lebanese government via Italy, and the Israeli conditions to stop the assault is release the 2 kidnapped troops, and hezbollah must be removed from the southern Lebanese border.
No more demand that UN 1559 be carried out.
The conditions are tough enough when you know that the government of Lebanon is unable to meet them.
UN 1559 cannot be enforced by Lebanon. Nor can they remove Hezbollah from their southern border. So it will be up the the Israelis to do it for them and this will require the continuing bombardment of Hezbollah in Beirut, in the Bekka Valley and in Southern Lebanon and the destruction of key elements of the Lebanese infrastructure.