The fermionic sub-programme of Cosmochrony locates the three-generation mass split in the J₃-odd part of the squared projective endomorphism E_² restricted to the gauge-singlet generation triplet C³₆₄₍, parametrised by a single real number u through E_²|₂℃_{₆₄₍}=diag (1, 12+u, 12-u), with the even sector diag (1, 12, 12) already closed by Born–Infeld parity. This note fixes the structural status of u before any explicit construction of E_. First, the projected Dirac square admits a universal Feshbach/Schur form E_=-S\, D\, (1-P) \, D\, S^*=-M^M with P=S^*S, exhibiting E_ as the Schur complement of the spinorial directions eliminated by the non-injective projection, negative semi-definite and vanishing in the injective limit. Second, the chiral block decomposition shows that u is controlled by the D^-transported, generation-projected part of the antiunitary chiral equivariance defect \ _ (P) =₋₋-\, ₑₑ\, ^-1 \ of the eliminated block 1-P, rather than by a naive block difference. Third, the minimal non-injectivity c q-c is chirally symmetric, so u=0 at the level of axioms A1–A3; a non-zero u requires a chiral symmetry-breaking that can originate only in the projection-locking axiom A4. The Seeley–DeWitt conventions are locked so that the operator-level and spectral-level definitions of u coincide on the flat effective metric, and a no-go result establishes that u is not accessible to any finite front observable because chirality is a Lorentzian rather than a finite-fibre datum. The remaining open deliverable is reduced to three sharp questions about A4.
Jérôme Beau (Sat,) studied this question.