Finite cyclicity of the quadratic graphic $I_{6b}^1$ in its full five-parameter quadratic unfolding

Version 2.0.0 replaces the previous article–supplement pair with one self-contained 119-page preprint. The record contains exactly three publication artifacts: the complete preprint PDF, a curated SymPy archive checking selected exact algebraic identities, and a curated Lean 4 archive checking selected exact algebra and conditional zero-transfer/counting interfaces. The paper proves local finite cyclicity of the compactified quadratic graphic I6b1 in its full five-parameter quadratic unfolding. The proof combines an exact-once first-hit decomposition, scalarization of two coupled four-passage matching equations, exact division by the transverse center ideal, compactification of the passage-scale ratio, boundary conjugacy, and a zero-radius Liénard reduction. The bound is uniform near every fixed B0 in (1/2,1), including B0=3/4, but is not asserted to be optimal. The Python and Lean supplements verify selected exact calculations and conditional logical interfaces; they do not formalize the parameter-uniform Dulac estimates, return geometry, global Liénard argument, or the main finite-cyclicity theorem.