San-lun

Saunders, in Buddhism in Japan, provides interesting detail on the "three treatises" of this school in his discussion of its Japanese counterpart, the Sanron. (ref. pp 115-116)

The Treatise on the Middle Way was aimed at refuting the "'wrong views' of the Hīnayāna."
The Treatise on the Twelve Gates was aimed at "correcting the errors of the Mahāyānists."
The One Hundred Verse Treatise was a "refutation of the heretical views of Brāhmanism."

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Chi-tsang's Buddha Nature

Interesting article in a JIABS from 1980 that discusses the basis for the doctrine that even inanimate objects possess buddha nature.

A couple of relevant quotations here:

Although there was no doctrinal precedent for Chi-tsang's assertion, in his examination of Buddhist texts he found several passages to substantiate his theory of a comprehensive Buddha-nature. As we shall see, Chi-tsang took a highly qualified step in expanding the notion of
salvation to include all of the natural, phenomenal world. As a San-lun scholar, however, Chi-tsang was neither interested, in a Taoist sort of way, in elevating nature to a religious dimension, nor simply concerned with the Nirvana-sutra anthropocentrically-limited promise of eventual enlightenment. Rather, Chi-tsang's most significant contribution to the discussion lay in his assertion that the Buddha-nature was a synonym for the middle path doctrine. The route by which he came to his expanded conception of Buddha-nature, then, was based on his primary view of prajna, and it is this that we wish to investigate in what follows.

Based on his own reading of the Nirvana-sutra, Chi-tsang also felt that the earlier theories ignored the Prajnaparamita doctrine articulated in the "Bodhisattva Lion's Roar" chapter on the identity of prajna and Buddha-nature, viz., "The Buddha-nature is called the first principle of emptiness; the first principle of emptiness is called prajna"