Turkic Beilik
In the work "Hudud al-'alam," the word "Turk" appears as the name of a tribe or some ethnic community. It is quite possible that here we encounter a mention of the proto-Qarakhanids, which, in turn, may support the idea that the population of the "Talas" beilik (domain) already referred to themselves with the term "Turk." This domain can also be referred to as the "Turkic" beilik. Incidentally, in one place in "Hudud al-'alam," it is stated that the Kyrgyz (likely "Tian Shan") and the Karluks (also likely Tian Shan) are in direct contact with each other, while in another, the lands of the Chigils and Turks lie between them. "There is also a discrepancy in the description of the borders between the Chigils and the Turks." Apparently, the Turks here should be understood as the proto-Qarakhanids or already the Qarakhanids. This, in turn, may confirm that the ethnic Chigils, the "Tian Shan" Kyrgyz, and the Tian Shan Karluks later became part of the formation of "Turk," and that the Qarakhanid dynasty could not have originated from them. Furthermore, from the information provided above, it is evident that the Turks are contrasted with the Chigils, Karluks, and Kyrgyz ("Tian Shan"), which may also support the conclusions we have drawn above.
We do not know how the process of forming the union of the Qarakhanid Turks took place. However, it can be assumed that the proto-Qarakhanids, who may have already been referred to as Turks, could have either conquered or subjugated the local tribes of Central Tian Shan or that related tribes of this region could have voluntarily joined them (the Kara-Khanid threat?), i.e., the Qarakhanid tribal union was voluntary, initiated by the proto-Qarakhanids — the Turks. Although it is also possible that the process of forming this union could have occurred through the use of force and on a purely voluntary basis.
