The command to carry the skull — Shiva Purana 3.8.61-62

This is the verse that turns a beheading into a discipline. Shiva does not absolve Bhairava; he instructs him to carry the skull and to perform the expiation vratam lokāya darśaya — as a showing, for the world. The penance is staged as instruction, and the Purana says so in as many words. That framing is what made the Kāpālika observance possible. The rite described here — living outside settled society, begging with a skull as the only bowl — was taken up as an actual twelve-year discipline in the Kāpālika lineages and continues within Aghora practice, explicitly as walking where Bhairava walked. The deity's biography is the vow's charter. vaidhasa, 'of the creator', is a derivative of Vedhas, a name of Brahma. The word choice matters: the text keeps naming whose skull it is, rather than letting it become a generic kapāla. A god carrying the skull of the creator of the universe is the image the tradition wants held in view. Nīlalohita, 'blue-and-red', is the name Brahma had used for him in verse 42 while claiming to be his father. Shiva uses it here in the course of giving him an office. The repetition is pointed.