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Arthur742Ramos/finite-graph-fundamental-group

Arthur Freitas Ramos, David Hulak, Ruy de Queiroz

Palomar Registrypalomar/PALOMAR-2026-08-27-000004Aug 27, 2026math.ATscore 0

Formalizes the fundamental group of a finite connected graph, represented as a finite weakly connected directed multigraph with its standard interval-cell quotient realization. The main result identifies the topological fundamental group at a chosen vertex with `FreeGroup (Fin (E + 1 - V))`. The proof compares the topological group with the endomorphism group at the root in Mathlib's free groupoid, whose explicit spanning-tree basis supplies the non-tree-edge generators. The development also proves the cycle-rank identities, root-change equivalences, the tree/triviality criterion, and the…

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