Steven Runciman's book on the First Bulgarian Empire, for instance, includes a pedigree of Kubrat from Attila's youngest son, Ernakh, as the Bulgarian khans apparently believed to have been descended from Attila. While no sources are cited and intermediate generations are missing, there is another complication in the Bulgarian route: no documented link between the Bulgarian dynasty and Charlemagne.
Christian Settipani suggested a more plausible descent, although it cannot be reconstructed generation by generation as well. The scholar gives credit to the traditional claim that Attila's daughter was one of many wives of Ardaric, king of the Gepids. It is assumed that the 6th-century Gepid rulers descended from Ardaric and that some royal Gepids claimed descent from this marriage in particular, although details are unclear.
A key link is the documented alliance between a Gepid princess Austrigusa and Waccho, king of the Lombards. According to Settipani, Waccho and Austricusa were ancestors of either Charlemagne's mother or his father, but this claim involves a considerable degree of speculation as well.
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