Refuting Peled et al.'s Section IV conjectures after Theorems 1 and 3, Eqs. (10) and (12): sharp fourth-order bounds without filter normal form

We refute the conjectures in Section IV immediately after Theorems 1 and 3, Eqs. (10) and (12), of Peled, Te'eni, Carmi and Cohen, Scientific Reports 11, 2849 (2021), that filter normal form can be removed from their correlation-minor bounds. Explicit separable states give robust violations in dimensions 2 by 4 and 2 by D for 5<=D<=8, including positive-definite examples. For every D>=4 and every Schatten parameter, the sharp fourth-order separable bound without filter normal form is 1/(192 sqrt(3)), attained by tetrahedral qubit projectors paired with four orthogonal flags. No common-size pair of regular coherent degree-1 pure designs exists in dimensions 2 and D>=5. We also correct the missing square root in arXiv:2005.12079v2, Appendix D.5, Eq. (D31), using the known separable covariance inequality. The original filter-normal-form theorems retain their scope.