In this excerpt from the Vayaviya Samhita of the Shiva Purana, various time scales are described:
Brahma's one day is equivalent to a kalpa. He is of unmanifest origin. A thousand kalpas make a year of Brahma. A Brahma's yuga comprises of eight thousand Brahma years. A thousand Brahma yugas make one Savana of Brahma. Brahma's life span consists of three thousand and three Savanas.... A day of Vishnu is the life time of Brahma. A day of Rudra is equivalent to the life time of Vishnu. A day of Sadashiva is life period of Shiva. A day of Sakshat Shiva is the life period of Sadashiva. The life time of Sadashiva is equal to the life period of five hundred and forty thousand of the previous deities. This function of time has been directed by Sakshat Shiva.
This has some discrepancies with time scales given in other scriptures; see my answer here. But my question is about the hierarchy of gods described in this chapter. Most of it is not surprising from a Shaivite perspective; the Shaiva Agamas say that the order of the gods from lowest to highest is Brahma, Vishnu, Rudra, Maheshwara, and Sadashiva.
But my question is, who is this "Sakshat Shiva" whose one day is equivalent to the entire lifetime of Sadashiva? My understanding is that Shaivites equate Sadashiva with the supreme Brahman, in the same way that that Vaishnavas believe the supreme Brahman is Para Vasudeva (see my answer here). So how can there be a being called Sakshat Shiva is who is superior to Sadashiva?
Are there any other scriptures which discuss Sakshat Shiva and his relation to Sadashiva? Also, this answer suggests that the Turiya state of the Upanishads is associated with Maheshwara, and that the Turiyatita state which I discuss here is associated with Sadashiva. So do Shaivites believe in a state of consciousness higher than Turiyatita, associated with Sakshat Shiva?