Unrestricted Two-Qubit Fourth-Resolvent-Moment Tensorisation

We establish a fourth-resolvent-moment tensorisation inequality with sharp constant 3 for arbitrary positive-definite qubit averages and traceless Hermitian qubit signals, without restrictions on spectral contrast, commutativity, or signal orientation. The proof combines an exact Dirichlet covariance representation, positivity of mixed spectral coefficients, majorization-based association, and a nonnegative orientation covariance. The result extends fourth-order tensorisation beyond the structural classes addressed in our earlier work on sharp quantum information combining. It does not establish the full unrestricted Hirche–Reeb entropy conjecture, which requires additional control beyond the fourth resolvent moment.