Refuting the trace-distance case of axiom (T4) of Denis, Lacaille, Martin and Serrano-Ensástiga

We refute the trace-distance case of axiom (T4) of Denis, Lacaille, Martin and Serrano-Ensástiga (arXiv:2605.29436v1, Section III.A.2, Eq. (22) with p=1; (T4) in Section II.B, Eqs. (7)–(8)), where "a proof is left open." An explicit SU(2)-covariant channel decreases the order-seven anticoherence of a mixed spin-four state by exactly 95/90552, disproving the universal validity suggested by their reported numerical evidence. The channel is a normalized sum of quadrupole Kraus operations; its covariance and trace preservation follow from Cartesian tensor identities. Both reduced states are diagonal, so the strict inequality reduces to rational arithmetic. We reconstruct an existing spin-four witness and give a self-contained exact counterexample within the full mixed-state domain of the proposed axiom.