Mahayana Buddha-nature, ‘buddhadhātu’, can only exist in the Buddha-Matrix ‘Tathāgatagarbha’ (source)
Only through bodhicitta can a sentient being know its buddha nature
!Koans often assume that the student is well versed in Mahayana doctrine, and the recorded koans that have become famous, are from those dialogs and teachings in which such doctrine was well drilled into the heads of the students. This however is NOT the case today with Students of the Way.
A dog though may have Buddha-nature, is unable to ‘muster up’ Bodhicitta. Thus, Joshu saying ‘Mu’ as a reply is doctrinally correct.
.A monk asked Joshu, a Chinese Zen master: `Has a dog Buddha-nature or not?’ Joshu answered: `Mu.’ [Mu is the negative symbol in Chinese, meaning `No-thing’ or `Nay’.]
The Tathāgatagarbha doctrine is essential for the Mahayanist to master. This is a metaphysics of the Bodhisattva and without at least familiarizing yourself with the basics of Mayanaya doctrine you end up with a very incomplete and lacking understanding of the Path.
[The Buddha said,] Now, Mahāmati, what is perfect knowledge? It is realised when one casts aside the discriminating notions of form, name, reality, and character; it is the inner realisation by noble wisdom. This perfect knowledge, Mahāmati, is the essence of the Tathāgata-garbha. – The Lankavatara Sutra