What is the authenticity of the Hadith that states the reason for ritual ablution (wudu) being for four limbs is Adam's—peace be upon him—disobedience when he ate from the forbidden tree?

This hadith has no basis. The Shiites mention it in their books with an unsound chain of transmission, and it contains weak narrators and unknown individuals even according to their own methodology. The Shiites have extensively fabricated lies against Ja'far al-Sadiq. What confirms the invalidity of this hadith is that the hadiths on the virtues of ablution mention the purification of the one performing ablution from their sins through washing their limbs, without mentioning anything of what was stated in the question.