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

Version 3.0.0 is a single self-contained 113-page preprint. This revision replaces the former multi-range four-passage argument with a direct estimate on the full positive product leaf and clarifies the first-hit partition, center-ideal division, complementary returns, and zero-radius Liénard argument. The paper studies local finite cyclicity of the compactified quadratic graphic I6b1 in its full five-parameter quadratic unfolding for each fixed B0 in (1/2,1), including B0=3/4; no optimality is asserted. The accompanying Python and Lean archives check selected exact algebraic identities and conditional logical interfaces. They do not formalize the parameter-uniform Dulac estimates, return geometry, global Liénard argument, or the main finite-cyclicity theorem.