Mathlib Polynomial Certification Bound: Mathlibs's Polynomial Machinery Does Not Support Certification Over Non-Simply-Connected Bases

We prove that Mathlib's \texttt{CategoryTheory.Polynomial} functor machinery does not support certification of $J$-elimination over non-simply-connected bases. All four rigidity audits fail: the polynomial functor definition places no constraint on $\Aut(B)$ (AUT-AUDIT), no proof of equivariance under base automorphisms exists in Mathlib (MON-AUDIT), the $J$-eliminator is stuck on non-reflexivity paths through polynomial transport (LIFT-AUDIT), and polynomial functor substitution is propositional rather than definitional (SUBST-AUDIT). We exhibit a concrete counterexample ($B = B\mathbb{Z}/2$) in which the Lean kernel's computation ($J(\refl, c) \equiv c$) diverges from the semantic model's transport ($J(\gamma, c) = \mathrm{swap}(c) \neq c$). The ``Certified'' claim of Nawrocki et al.\ (CPP 2026), which bases its formalization on Mathlib's categorical machinery, is bounded to models with $\pi_1(B) = 0$---a condition not disclosed in the paper or in the deliverables of the supporting federal grants (AFOSR MURI FA9550-21-1-0009, NSF 2434614). This paper answers the question posed in the Dimensional Bound audit (Eden, January 2026): Mathlib's polynomial machinery is not stable under non-trivial automorphisms of the base object.