As I discuss in my question here, Vishnu is said to have taught the principles of Vaishnavism to four disciples: Lakshmi, Brahma, Shiva and Sanatkumara. And in turn they started the four main Sampradayas or traditions of Vaishnavism: Sri Sampradayam (which I belong to), Brahma Sampradayam, Rudra Sampradayam, and Kumara Sampradayam. My question is about the Rudra Sampradayam, the one founded by Shiva.
The most famous Acharya associated with the Rudra Sampradayam is Vallabhacharya, the founder of the Pushtimarg sect which worships the Srinathji form of Krishna (which I discuss here). The reason that Vallabhacharya's followers consider themselves part of the Rudra Sampradayam is they believe that Vallabhacharya was in the disciplic succession of Vishnusvami, an earlier Vaishnava Acharya associated with the Rudra Sampradayam. But in this journal paper, G. H. Bhatt argues that Vallabacharya did not actually belong to the disciplic succession of Vishnusvami, and that Vishnusvami believed in a dualistic philosophy that has no connection to Vallabacharya's philosophy of Shuddhadvaita. So my question is, what surviving works of the Rudra Sampradayam are there from before the time of Vallabhacharya? That should help settle the issue.
This chapter of Vidyaranya's Sarva Darshana Sangraha, written contains some references to works from Vishnuswami's sect. The context is that Vidyaranya is discussing a Shaivite sect called the Raseshvaras, who believed in using Mercury to make the body immortal and thereby achieve Jivanmukti. The Raseshvaras argue that it's possible for a body to be eternal, because Vishnuswami's sect says the body of Vishnu's incarnation Narasimha is eternal:
And this is not to be supposed to be unprecedented, for the adherents of the doctrine of Vishnusvámin maintain the eternity of the body of Vishnu half-man and halflion. Thus it is said in the Sákára-siddhi - “I glorify the man-lion set forth by Vishnusvámin, whose only body is existence, intelligence, and eternal and inconceivably perfect beatitude.” If the objection be raised that the body of the man-lion, which appears as composite and as coloured, is incompatible with real existence, it may be replied: How can the body of the man-lion be otherwise than really existent, proved as it is by three kinds of proof: (1) by the intuition of Sanaka and others; (2) by Vedic texts such as, A thousand heads has Purusha; and (3) by Purānic texts such as, That wondrous child, lotus-eyed, four-armed, armed with the conch-shell, the club, and other weapons? Real existence and other like predicates are affirmed also by Srikántamišra, the devoted adherent of Vishnusvámin. Let, then, those who aspire to the highest end of personal souls be assured that the eternity of the body which we are setting forth is by no means a mere innovation.
So do the Sakara Siddhi or the works of Srikantamishra still exist?
Also, I've seen claims that Sridharaswami was an Acharya of the Rudra Sampradayam who lived between the time of Vishnuswami and the time of Vallabhacharya. Can anyone verify if that's correct? If so, his commentaries on the Bhagavad Gita and the Srimad Bhagavatam still exist. But I've seen claims that there are multiple Sridharaswamis, so the one who lived before Vallabhacharya may not belong to the Rudra Sampradayam. In any case, other than the works of Sridharaswami, are there any other works of the Rudra Sampradayam before the time of Vallabhacharya?
EDIT: In this section of the ISKCON commentary on the Chaitanya Charitamrita, Srila Prabhupada claims that Vishnuswami wrote a commentary on the Brahma Sutras called the Sarvajna Bhashya. Is that correct? If so, I assume it no longer exists.