Is the Eid al-Adha prayer obligatory on Wednesday, according to the Kingdom of Saudi Arabia, or on Thursday, according to the Islamic Center in Japan, knowing that we fast on the Day of Arafat and offer sacrifices?

The decisive factor is the sighting of the Dhu al-Hijjah crescent in the questioner's country. Based on this sighting, the fasting of the ninth day and Eid al-Adha are determined. The اختلاف المطالع (difference in moonrise locations) is considered valid, so it is not obligatory to follow Saudi Arabia's sighting if there is a difference in the moonrise locations.