Generally, Vaishnavas follow the Pancharatra Agamas, Shaivites follow the Shaiva Agamas, and Shaktas follow the Shaiva Agamas. But long ago, there was a group of people in Kashmir who followed the Shakta Agamas but adopted Shiva as their Ishta Devata. That group evolved into what we now call Kashmir Shaivism. Because it has its roots in Shakta Agamas, it subscribes to a monistic philosophy, as opposed to philosophical Shaivite sects like Shaiva Siddhanta which are more dualistic in their philosophy.
Now the most famous Kashmiri Shaivite philosopher was Abhinavagupta, who lived in the 10th century. As I discuss in this question, Abhinavagupta had many gurus, but one of them was Lakshmanagupta, whose guru was Utpaladeva, who is the subject of my question. Utpaladeva composed a work called the Ishwara Pratyabhijna Karika, which is the defining work of the Pratyabhijna school, a philosophical school founded by Utpaladeva's guru Somananda which involves regaining knowledge of one's own Shiva-nature. The Pratyabhijna school is one of the traditions that merged to form the Kashmiri Shaivite sect.
In any case, Utpaladeva wrote two commentaries on his own Ishwara Pratyabhijna Karika, the Vritti which is short and the Vivriti which is long. The Vritti still exists, and has been translated by Rafaelle Torella in this book. But the Utapaladeva's Vivriti is mostly lost now. That's because people stopped paying attention to it and started paying attention to Abhinavagupta's two commentaries on the Ishwara Pratyabhijna Karika, namely the Ishwara Pratyabhijna Vimarshini and the Ishwara Pratyabhijna Vivriti Vimarshini. That's ironic, because the latter work is actually a commentary on the Vivriti, but the problem is that Abhinavagupta seldom quotes the actual verses of the Vivriti in his commentary. And so the Vivriti was eventually lost.
But my question is, what surviving fragments of Utpaladeva's Ishwara Pratyabhijna Vivriti have been translated into English?