On the Internet, without any difficulties, you can find many different mantras of Kala Bhairava, but the specific source of origin of these mantras (Tantra, Agama, Grantha, etc.) is always not indicated. One gets the unpleasant impression that most of them are just someone's fiction.
Together with Chamunda das, we managed to find out the following.
In the Mahakala Samhita, Guhyakali Khanda 2, shloka 1063, the Bhairava mantra of nine syllables (navakshari) is described. Nama-bija (vibhakti samas) should be used in this mantra. Bhairava's name must be in the dative case. In shloka 1064 it is stated that the mantra should be closed with the word "namah" - https://archive.org/details/mahakalasamhitaguhyakalikhandakishornathjhapart2rashitriyasanskritsanstha_202003_632_X/page/n155/mode/2up
Therefore, the given canonical mantra of Kalabhairava is as follows: कां कालभैरवाय नमः
So, my question has been answered. This topic can be closed. Special thanks to Chamunda das.