Folding Edges into Vertices: A Machine-Checked Proof of Bass's Determinant Formula for the Ihara Zeta Function in Lean 4

A machine-checked proof, in Lean 4 / Mathlib, of Bass's determinant formula for the Ihara zeta function of a finite graph: (1-u^2)^|V| det(I-uB) = (1-u^2)^|E| det(I-uA+u^2(D-I)), where B is Hashimoto's non-backtracking operator on the 2|E| oriented edges. The headline theorem is sorry-free, depending only on propext, Classical.choice and Quot.sound, and is proved over a field. To the author's knowledge this is the first formalization of Bass's formula, of the non-backtracking operator, or of the Ihara-zeta reciprocal det(I-uB) in any proof assistant. It is the companion Ihara/cycle side to the author's matching-polynomial formalizations 'Random Signs into Matchings' (Godsil-Gutman) and 'Unfolding a Graph into a Tree' (Heilmann-Lieb). English and Spanish editions are included.