Sage Sankrithi is the founder Rishi of the Sankrithi Gotra. The lineage of Sankrithi's is given as Shakthya, Sankrithya, and Gauriveetha. i.e. lineage of Shakthi, Sankrithi, and Gauriveethi.

Sankrithi is the Grandson of Sage Vashishta, and the son of Sage Shakthi. Incidentally, Sage Shakthi is the father of Sage Parashara

Parashara

' is a Rigvedic Maharishi and author of many ancient Indian texts. Parāśara was the grandson of Vashista, the son of Śakti Maharṣi, and the father of Vyasa. There are several texts which give reference to Parāśara as an author/speaker...

 (the father of Sage Veda Vyasa

Vyasa

Vyasa is a central and revered figure in most Hindu traditions. He is also sometimes called Veda Vyasa , or Krishna Dvaipayana...

.)

There is not much known about Sage Sankrithi except that his name figures in the Avadhuta Upanishad

Upanishad

The Upanishads are philosophical texts considered to be an early source of Hindu religion. More than 200 are known, of which the first dozen or so, the oldest and most important, are variously referred to as the principal, main or old Upanishads...

, where Lord Dattatreya

Dattatreya

Dattatreya or Datta is a Hindu deity encompassing the trinity of Brahma, Vishnu and Shiva, collectively known as Trimurti. The name Dattatreya can be divided into two words - "Datta" and "Atreya" referring to the sage Atri, his physical father.Various Hindu sects worship him differently...

explains the nature of an Avadhuta to Sage Sankrithi.

Our Gotra is Sankrut or Sankrit that is what we know from our forefathers,may be it is from Sankrithi-we are audhichya tolak brahmins in gujarat-jd joshi