Isma'il ibn Ja'far in the context of "Muhammad al-Taqi"

The doctrine of the Imamate in Isma'ilism differs from that of the Twelvers because the Isma'ilis had living Imams for centuries after the last Twelver Imam went into concealment. They followed Isma'il ibn Ja'far, elder brother of Musa al-Kadhim, as the rightful Imam after his father, Ja'far al-Sadiq. The Ismailis believe that whether Imam Ismail did or did not die before Imam Ja'far, he had passed on the mantle of the imamate to his son Muhammad ibn Isma'il as the next imam.

Abū Aḥmad ʿAbd Allāh ibn Muḥammad ibn Ismāʿīl (Arabic: أَبُو أَحْمَد عَبْد ٱللَّٰه ٱبْن مُحَمَّد ٱبْن إسْماعِيل, c. 766 – 828), was a descendant of the Islamic prophet Muhammad and the eight of the Isma'ili Imams, succeeding his father, Muhammad ibn Isma'il (d. 813). Abd Allah traveled throughout Persia and the Middle East. At an unknown date, in the first half of the 3rd/9th century, he found refuge in Syria, where he eventually re-established contact with some of his da'is, and settled in Salamiyah, continuing to pose as a Hashimite merchant. Abd Allah did not reveal his true identity publicly and only a few high ranking Isma'ili hujjats and da'is were aware of his whereabouts. He is known by the epithets al-Wāfī (lit. 'true to one's word') and al-Raḍī (lit. 'the satisfied one'). Abd Allah designated his son Ahmad as his successor and died around 828.

With the death of Ja'far al-Sadiq in 148/765, Isma'il (d. 158/775) and Muhammad (d. 197/813), the gravity of persecutions of the Abbasids had considerably increased. The Isma'ili Imams were impelled to thicken their hiding, therefore, the first dawr al-satr came into force from 197/813 to 268/882, wherein the Imams were known as al-a'imma al-masturin (lit. 'the concealed Imams'). The concealment ended with the establishment of the Fatimid caliphate (r. 909–1171).