{"id":"palomar/PALOMAR-2026-09-02-000013","url":"https://github.com/DhyeyMavani2003/chip-firing-with-lean/tree/5b422d855c02af60591121ba7c11b5e8242542b8","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-02-000013-v1.json","repo":"https://github.com/DhyeyMavani2003/chip-firing-with-lean","tags":["math.CO","msc:05C57","msc:14T20","graph-theory","riemann-roch","lean-formalization"],"score":0,"title":"Chip-Firing with Lean 4","trust":"high","domain":"math.CO","source":"palomar","authors":["Dhyey Dharmendrakumar Mavani","Nathan Pflueger"],"reviews":0,"subject":"math.CO","summary":"A Lean 4 / Mathlib formalization of Baker and Norine's Riemann-Roch theorem for finite graphs. Chip configurations on a finite graph, modulo chip-firing moves, form an abelian group analogous to the group of line bundles on a compact Riemann surface. Each class can be assigned a rank, analogous to the dimension of a linear series. These ranks then satisfy a formula of the form r(D) - r(K-D) = deg D + 1 - g, in exact analogy to Riemann surfaces. This formula is formalized, along with the analog of Clifford's theorem for finite graphs.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-02","reactions":{},"formalized":true,"formalizes":[{"title":"Riemann-Roch and Abel-Jacobi theory on a finite graph","identifier":"https://doi.org/10.1016/j.aim.2007.04.012","relationship":"formalizes"}]}