Lean Modulus

by Nathan Albin

Formalizations, in Lean 4 and Mathlib, of results from research on graphs, networks, and the modulus of families of objects. This is a working project — results are added incrementally, and the blueprint below tracks what’s genuinely proved versus proved with sorry.

Papers

Paper Status Lean source
Fairest Edge Usage and Minimum Expected Overlap for Random Spanning Trees (Albin, Clemens, Hoare, Poggi-Corradini, Sit, Tymochko, 2021) 🚧 just started LeanModulus/Papers/FairestEdgeUsage

More papers will be added here as they’re formalized.

Dependency graph

Each node below is a definition or theorem from the blueprint; colors show what’s formalized, what’s ready to formalize next, and what’s still blocked. Click a node to see its statement. Check the legend for color coding. You can also view the full-page version. This graph, the blueprint pages it’s embedded in, and the proved/sorry tracking throughout this site are all generated by leanblueprint.

Resources

Why formalize this

I’m moving toward including Lean theorem proving in my courses and my research workflow. Formalizing results from my recent papers is a way for me to practice writing Lean proofs for real mathematical content rather than textbook exercises. It also gives me a chance to explore the various AI tools for Lean, and to see how well they can help with real research-level mathematics.