Multi-agent Autoformalization of Tensor Network Theory
This work addresses the lack of formal verification for foundational results in tensor network theory—such as the fundamental theorem of matrix product states—and the challenge of preserving mathematical intent during large-scale autoformalization. To this end, it introduces the first multi-agent collaborative framework for the automatic formalization of complex physical theories. Built upon the Lean theorem prover, the framework integrates domain-specialized large language model agents, structured mathematical blueprints, and a human-in-the-loop review mechanism. It successfully formalizes the fundamental theorem of matrix product states, uncovers a novel proof pathway absent from the literature, and extends formalization to physical concepts like symmetry-protected topological phases. The project also establishes TNLean, the first library for tensor networks and quantum information in Mathlib, with all code and formalization blueprints publicly released.