Formally Verified Patent Analysis via Dependent Type Theory: Machine-Checkable Certificates from a Hybrid AI + Lean 4 Pipeline

Researcher George Koomullil has introduced a novel, formally verified framework for patent analysis that combines AI with the Lean 4 interactive theorem prover. The system, detailed in a 100-page arXiv paper, addresses a critical gap in intellectual property law by moving beyond slow manual analysis and opaque probabilistic AI models. It formalizes five complex legal analyses—patent-to-product mapping, freedom-to-operate, claim construction sensitivity, cross-claim consistency, and doctrine of equivalents—into six verifiable algorithms. The core innovation is a hybrid pipeline where an AI layer first generates match scores between claims and products, and then a Lean 4-based system mathematically verifies all downstream legal reasoning.

The framework's DAG-coverage core algorithm is fully machine-verified in Lean 4, a proof assistant based on dependent type theory. Patent claims are encoded as directed acyclic graphs (DAGs), and match strengths are treated as elements of a verified mathematical lattice. Confidence scores then propagate through claim dependencies via proven-correct monotone functions. This creates machine-checkable certificates for legal conclusions, a first for the IP field. However, the paper is clear that the system's guarantees are conditional: it certifies the mathematical correctness of computations *downstream* of the initial AI scores, not the accuracy of the scores themselves. A case study on a synthetic memory-module claim demonstrates the approach, though validation against real adjudicated cases remains future work.