Small counterexamples to the two-polynomial criterion for Ur-equivalence

The two-polynomial criterion for Ur-equivalence proposed by Browning, Hopkins and Kelley fails for a pair of five-point posets with isomorphic deletions: replacing the marked points by a two-element antichain gives order-preserving map counts 138 and 140 at three. A six-point example keeps the ambient poset fixed, while an eight-point path-shaped poset has two minimal points in different automorphism orbits with isomorphic deletions and substitution counts 909 and 911. Elementary finite counting arguments explain the failure through differing second moments of the substitution response. The principal results are reported with candidate status; no minimum-size or uniqueness claim is made.