On Family-Separated Seesaw Relations: Exact Reconstruction and Corrections

We examine the family-separated seesaw (FSS) ansatz proposed in arXiv:2605.27049v2. Combining its paired cancellations with exact partial unitarity fixes the light and heavy mixing blocks in terms of one unitary matrix and the paired mass ratios. We classify their unitary completions and reconstruct the Dirac and singlet Majorana mass matrices, distinguishing the physical heavy masses from the singlet mass parameters. This identifies FSS as an exact realization of form dominance whose conventional one-loop leptogenesis cancellation is already established. The particular sum of lepton-number-violating invariants entering the proposed decay asymmetry therefore vanishes; individual CP invariants need not vanish. We also correct the heavy-mass reconstruction formulas and quantify their errors for both light-mass orderings. These formulas are conditional algebraic relations, not independent predictions of the heavy spectrum. Numerical mass–mixing illustrations, explicit chiral projections for double-beta decay, and a leading-logarithmic estimate of radiative misalignment clarify the physical reach and limitations. The contribution is an exact consistency analysis and correction of specific proposed consequences rather than a new mass-generation mechanism or a general prohibition of leptogenesis.