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

Computer Science > Artificial Intelligence [Submitted on 20 Apr 2026] Formally Verified Patent Analysis via Dependent Type Theory: Machine-Checkable Certificates from a Hybrid AI + Lean 4 Pipeline George Koomullil We present a formally verified framework for patent analysis as a hybrid AI + Lean 4 pipeline. The DAG-coverage core (Algorithm 1b) is fully machine-verified once bounded match scores are fixed. Freedom-to-operate, claim-construction sensitivity, cross-claim consistency, and doctrine-of-equivalents analyses are formalized at the specification level with kernel-checked candidate certificates. Existing patent-analysis approaches rely on manual expert analysis (slow, non-scalable) or ML/NLP methods (probabilistic, opaque, non-compositional). To our knowledge, this is the first framework that applies interactive theorem proving based on dependent type theory to intellectual property analysis. Claims are encoded as DAGs in Lean 4, match strengths as elements of a verified complete lattice, and confidence scores propagate through dependencies via proven-correct monotone functions. We formalize five IP use cases (patent-to-product mapping, freedom-to-operate, claim construction sensitivity, cross-claim consistency, doctrine of equivalents) via six algorithms. Structural lemmas, the coverage-core generator, and the closed-path identity coverage = W_cov are machine-verified in Lean 4. Higher-level theorems for the other use cases remain informal proof sketches, and their proof-generation functions are architecturally mitigated (untrusted generators whose outputs are kernel-checked and sorry-free axiom-audited). Guarantees are conditional on the ML layer: they certify mathematical correctness of computations downstream of ML scores, not the accuracy of the scores themselves. A case study on a synthetic memory-module claim demonstrates weighted coverage and construction-sensitivity analysis. Validation against adjudicated cases is future work. Comments: 100 pages, 8 figures, 9 tables, 6 algorithms Subjects: Artificial Intelligence (cs.AI); Logic in Computer Science (cs.LO); Programming Languages (cs.PL) MSC classes: 68V15 ACM classes: F.4.1; I.2.3; K.5.1 Cite as: arXiv:2604.18882 [cs.AI]   (or arXiv:2604.18882v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2604.18882 Focus to learn more Submission history From: George Koomullil [view email] [v1] Mon, 20 Apr 2026 22:02:57 UTC (344 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-04 Change to browse by: cs cs.LO cs.PL References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)