Non-Invertibility and Emptiness: A Formal Reconstruction of the Madhyamaka Analysis of Identity

This work presents a mathematical and computational framework that formalizes a central insight of Madhyamaka philosophy: the absence of inherent identity. Using generative latent graph models, we show that observable relational structures can be produced by multiple distinct underlying configurations. This implies that no unique, inherently existing latent state can be identified from the data, providing a precise structural analogue of the Madhyamaka “object of negation.” Crucially, the space of possible underlying configurations is not arbitrary. Our experiments reveal that it is highly constrained and effectively low-dimensional, dominated by a single principal mode. This demonstrates that the absence of inherent existence does not lead to indeterminacy or chaos, but to a structured form of relational dependence. These results suggest that key Madhyamaka insights can be reformulated in precise mathematical terms: phenomena are not grounded in independently existing entities, yet they arise within a coherent and tightly constrained relational structure.