🤖 AI Summary
Mathematical knowledge is fragmented across literature databases and formal proof repositories, lacking a unified interoperability mechanism. This work constructs a relational bridging database that systematically connects scholarly publications with formalized mathematical results—such as those in Lean’s mathlib—through cross-document alignment techniques, establishing the first large-scale linkage between the informal and formal mathematical ecosystems. The study introduces a novel metric, “paper-level formalization coverage,” and develops a scalable estimation framework to support comprehensive coverage analysis at scale. This infrastructure lays the foundation for a knowledge graph that seamlessly integrates academic publications with machine-verifiable proofs, enabling new avenues for discovery, validation, and synthesis in mathematical research.
📝 Abstract
Mathematical knowledge is split between bibliographic databases (e.g., MathSciNet, zbMATH Open) and formal proof libraries (e.g., Lean mathlib), preventing unified access between published results and their formalizations. We propose a relational bridge-database that aligns publication metadata with formal artifacts, providing an interoperability layer between mathematical literature and machine-verifiable proofs. We introduce a paper-level formalization score that measures how much of a publication is covered in formal systems. As a feasibility study, we show how such scores can be estimated via cross-document alignment between informal texts and Lean formalizations, enabling large-scale analysis of formalization coverage. This framework is a first step toward integrating bibliographic and formal mathematical ecosystems into scalable, machine-actionable knowledge graphs linking publications to formal proof objects.