How did the Byzantine Empire recognize Bulgar control of land south of the Danube?

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The Byzantine Empire recognized Bulgar control of land south of the Danube River through a formal treaty signed in 681.12

Following the defeat of the Byzantine emperor Constantine IV by the Bulgars led by Asparukh, the empire was compelled to acknowledge the establishment of an independent Bulgarian kingdom. This agreement officially recognized Bulgar authority over the region situated between the Balkan Mountains and the Danube, marking the foundation of the first Bulgarian empire. Subsequent treaties in 705 and 716 further solidified this recognition, despite the territorial loss being viewed as a humiliation by the Byzantine state.123