{"id":"palomar/PALOMAR-2026-09-23-000004","url":"https://github.com/Arthur742Ramos/stallings-folding/tree/117dde0a8415d3da1787e15ad22a6223a744432d","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-23-000004-v1.json","repo":"https://github.com/Arthur742Ramos/stallings-folding","tags":["math.GR","math.LO","msc:20E05","msc:68Q45","msc:03B35","group-theory","free-groups","stallings-graphs","lean"],"score":0,"title":"Verified finite automata for finitely generated subgroups of F₂","trust":"high","domain":"math.GR","source":"palomar","authors":["Arthur Freitas Ramos"],"reviews":0,"subject":"math.GR","summary":"Source-based formalization of the classical Stallings finite-graph recognition theorem. It gives an executable finite folding construction for every finite list of words in the rank-two free group, with exact subgroup-membership correctness. The least deterministic fold congruence is computed by finite exhaustive search; there is no complexity claim or implementation of core trimming, subgroup bases, intersections, or index algorithms.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":true,"formalizes":[{"title":"Topology of Finite Graphs","identifier":"https://doi.org/10.1007/BF02095993","relationship":"formalizes"}]}