Chen and Zuo conjectured that the rth jet closure of the Jacobian ideal of a weighted homogeneous polynomial equals that ideal plus the (r+1)st power of the maximal ideal. For f=z(x^2+y^3), we exhibit xy^3 in the fourth jet closure but outside J(f)+(x,y,z)^5. Membership follows from an explicit identity in universal jet coefficients, and nonmembership from a homomorphism to k[s]/(s^10). We also give an irreducible four-variable example and a transfer principle for principal-ideal jet defects. The construction uses the published cusp example of de Fernex, Ein and Ishii. Both examples are nonisolated and disprove the conjecture as written, not a version restricted to isolated singularities. The all-orders OWR-4086-008 question is already resolved by Mallory and is not claimed as a new result of this note.
