I've seen both the Karluks and the Uyghurs referred as the founders of the Kara-Khanid Khanate (sometimes in the same source).
In this online guide created by Ulrich Theobald (Universität Tübingen) we find both:
Chinaknowledge.de: Uighurs claims it was founded by Uyghurs (see The Uyghurs of Kašgar).
Of course, I'm not discussing the ethnos of the population or its later leaders, only the founding members of the dynasty.
Is there a consensus about the matter or am I missing something?
The language of the Turkic literary works emanating from the Qara Xan empire (namely al-Kashgari and the Kutadgu Bilig) are not written in Uyghur (alias Old Turkish), but in a different branch of Turkic. Clauson, in his “Etymological Dictionary Of Pre-Thirteenth-Century Turkish” classifies it as Xaqani, not Uyghur. This means that it is problematic to identify the founders of the empire as Uyghurs.
Uyghur were Karluks and Karluks were Uyghurs , same people used different tribal name. Karluk is a Turkic language dialect branch which Uyghurs belonged to. Few tribes including Karluk (same as Uyghurs) built an empire and named it Uyghur empire. Uyghur meaning in early Turk language meaning is unification. After Uyghur empire taken over by Kirghiz, remaining Turks who used Uyghur name resided around Tarim basin. So Karluk tribe which Uyghurs came from originally, joined Uyghurs in Kashgar from Karluk Yabgu state, and built the empire Karakhanid. So later centuries after , land was devided with different empires and powers, so one Karluks(Uyghurs ) Turks became Uzbek (means self ruler or master or leader) under the leadership of Shaibani, and other Karluks went back to Uyghur name during Yarkent Kagnate. So Uyghurs of now and Uzbeks speak the same Turkic languages with accent difference. Also their clothing and culture is the same.
So during Karakhanids, Muslim Uyghur Turks who used Karluk term in Kashgar and Artux, defeated Neighbor Buddhists Uyghur kingdoms and united them.
So Uyghurs and Uzbeks of now belong to Karluk branch of Turkic language.