Kafadar, Cemal. Between Two Worlds: The Construction of the Ottoman State. 1995. с. xii. There is still not one authentic written document known from the time of ʿOsmān, and there are not many from the fourteenth century altogether.
Kafadar, Cemal. Between Two Worlds: The Construction of the Ottoman State. 1995. с. 122. The Ottoman historical tradition maintains, with some exceptions, that the tribe that later represented the core of Osman's earliest base of power came to Asia Minor in his grandfather's generation in the wake of the Chingisid conquest in central Asia. This makes chronological and historical sense, but otherwise the details of their story, including the identity of the grandfather, are too mythological to be taken for granted.
Kafadar, Cemal. Between Two Worlds: The Construction of the Ottoman State. 1995. с. 122. That they hailed from the Kayı branch of the Oğuz confederacy seems to be a creative „rediscovery“ in the genealogical concoction of the fifteenth century. It is missing not only in Ahmedi but also, and more importantly, in the Yahşi Fakih-Aşıkpaşazade narrative, which gives its own version of an elaborate genealogical family tree going back to Noah. If there was a particularly significant claim to Kayı lineage, it is hard to imagine that Yahşi Fakih would not have heard of it.