2026/04/26 by Xinze Li, Nanyun Peng, Simone Severini +1 · 1 voice
Computer Science · Mathematics · #Centrality #Dependency (UML) #Dependency graph #Graph #Graph theory #Logic, programming, and type systems #Mathematics, Computing, and Information Processing #Network analysis #Network science #Network structure #Network theory #Parallel Computing and Optimization Techniques #cs.LO #cs.PL #cs.SI #math.HO
paper · pdf · doi:10.48550/arxiv.2604.24797
openalex publication_date 2026/04/26 · arxiv published 2026/04/26 · openalex created_date 2026/04/30 · arxiv updated 2026/05/04 · openalex updated_date 2026/07/28
The ongoing development of Lean 4's Mathlib has produced a macroscopic structural complexity that interweaves logical, mathematical, and infrastructural dependencies. We present a network analysis of this library, extracting its dependency structure into a multilayer graph of 308,129 declarations, 8.4 million edges, and 7,563 modules. By introducing graph decompositions that isolate explicit edges from those synthesized by the compiler or driven by proofs, we quantify the structural properties of formalized mathematics. Our analysis reveals three findings. First, taxonomies designed by humans diverge from logical structures, exhibiting a 50.9% coupling across namespaces. Second, developers utilize a median of 1.6% of the imported scope. Third, formalization compresses semantic hierarchies, with network centrality capturing language infrastructure rather than mathematical relevance.