The following excerpt is from "Kapila Founder of Sankhya and Avatara of Vishnu" by Knut A Jacobsen, 2008, as far as I remember
there are similar Pramans in "Shree Padma-Purana" and "Shree Skanda-Purana":
there are similar Pramans in "Shree Padma-Purana" and "Shree Skanda-Purana":
"Another Kapilatirtha associated with cows is mentioned in the text with the interesting name Kapila-purana. The text does not contain any of the teachings of Kapila.
Instead, the text is mainly concerned with places of pilgrimage, although only one Kapilatirtha is mentioned.
This is the Kapilatirtha at Virajaksetra located on the river Vaitarani.
The text states that if one takes a bath at this Kapilatirtha on the fourteenth day of the Pitrpaksa both Parvati and Siva are pleased and one attains the fruit equal to the giving of a Kapila cow (a red-brown cow), and goes to Goloka.
These examples are telling about a possible origin of this group of tirthas. Perhaps the Kapila cow has given name to these sites. Sometimes later some of them became associated with the sage Kapila.
The most important pilgrimage centre today that connects Kapila to a cow or cows is Kapilatirtha in Tirupati, Andhra Pradesh.
Other than the Vatican, no pilgrimage site receives as many visitors in a year as the Vehkatesvara temple at Tirumala.
Kapilatirtha is situated at the base of the Tirumala hill where the road to Tirumala starts ascending. This tirtha marks the lower border of the sacred area of the Tirumala hill.
The main attraction of the Kapilatirtha is a beautiful waterfall.
A water tank and a temple complex have been built at the bottom of the waterfall. When going on a pilgrimage to Tirumala, it is common, to stop at the Kapilatirtha to bathe under the waterfall. This is said to cleanse one from moral impurity and give religious merit.
The temple of the Kapilatirtha which is next to the water tank, houses a linga. This linga manifested itself because of Kapila’s worship of Siva, according to the temple’s foundation narrative.
After the linga had manifested itself, a cow used to come every day to stand over the linga. Milk then flowed from its udders down on the linga. On the wall next to the svayambhu linga in the Kapilesvara Mandir, there is now a painting of this scene with Kapila sitting next to it.
This image has been reproduced in the flower beds in the beautiful park outside of the temple. According to another foundation myth, Siva requested that he be allowed to stay on the Tirumala hill.
The God Vishnu then allotted him (Shiva) a place at the banks of the Kapilatirtha where the linga now is worshipped. In an inscription dating from between ec 1011 to 1044, a Kapilesvara temple known as the Kapilatirtha is referred to.
The sage Kapila is usually not called Kapilesvara, but the reference could possibly be to this sage. Another inscription states that the tank was provided with stone steps all around in 1531.
A ninteenth-century description of the temple, mentions that a wooden cow, a calf and Kapila Mahamuni were placed on top of a three foot high anthill in the temple.
By then certainly Kapila had taken on the role he has today at this tirtha".
Cited from
"Kapila Founder of Sankhya and Avatara of Vishnu"
by Knut A Jacobsen, 2008, p. 169-171
