As salaamu alaykum, Looking at the arabic it refers to the hilal and it doesn't refer to the 'birth of the new moon' or 'astronomical new moon' which cannot be sighted nor can it be classified as 'Hilal'. Conflating the two can be a source of confusion. Whoever sees the hilal should begin fasting for ramadan whether or not his testimony is accepted or not, and in relation to this eighth factor, that if someone is positive by some means that the month has begun -ru'ya, khabar, or [in his statement] hisaab then they should begin fasting. The end of the month has a different Hukm. Even if you have seen the moon with your own eyes you are not permitted to stop fasting if your testimony is not accepted. wallahu alim