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He became Bagrat's immediate successor, but he must have been a rather insignificant ruler since he had no official title. He had a posthumous son also called Gurgen who died in 968.
References
Cyrille Toumanoff, Les dynasties de la Caucasie chrétienne de l'Antiquité jusqu'au XIXe siècle : Tables généalogiques et chronologiques, Rome, 1990