Concept:
The phrase "Catuṣkoṭi-Vinirmuktaṃ Tattvaṃ" refers to the "Truth that is free from the four-fold logic" (is, is not, both, neither). This is the hallmark of the Mādhyamika (Middle Way) school founded by Nagarjuna. However, several scholars and Vedantins, most notably Gaudapada, observed a striking structural and philosophical similarity between this Buddhist dialectic and the descriptions of the "Turiya" (the fourth state) in specific Vedic texts.
Step 1: Analyzing the Māṇḍūkyopaniṣad and the Fourth State.
The Māṇḍūkyopaniṣad is the shortest of the major Upanishads and focuses entirely on the syllable "OM" and the four states of consciousness: waking, dreaming, deep sleep, and the Turiya. The Turiya is described negatively (Neti-Neti style): it is not internal awareness, not external, not both, not a mass of consciousness. This "via negativa" approach and the description of Reality as being beyond all categories closely mirrors the Mādhyamika concept of *Shunyata* (Emptiness) which is also "Catuṣkoṭi-Vinirmukta" (beyond the four positions of existence, non-existence, etc.).
Step 2: Historical linkage through Gaudapada.
Gaudapada, the teacher of Shankara's teacher, wrote the *Māṇḍūkya Kārikā*. In this text, he uses language and logical structures that are so similar to Mādhyamika Buddhism that he is often called a "Prachanna Bauddha" (Hidden Buddhist). He argues that the ultimate reality (Atman/Brahman) described in the Māṇḍūkyopaniṣad is "Ajativada" (Non-origination), which aligns perfectly with the Mādhyamika sense that the absolute truth cannot be grasped by the four-fold logical alternatives.