Projected Yukawa Line and Generation-Level Assignment

This note opens the mass-sector frontier of the fermionic-matter sub-programme of Cosmochrony, and closes only its first stage. It does not derive the three-generation masses, the Yukawa couplings, or the mixing. It isolates two structural results that the admissible spinor carrier already determines, and separates them sharply from the mass normalisation that does not yet follow. First, on the rank-two admissible spinor bundle ${\mathcal{S}_{\Pi}}$ produced by the Lorentzian complexification of the metaplectic Weil carrier of Q14, the determinant line ${L_{Y}}:= \wedge^{2}({\mathcal{S}_{\Pi}})$ is the unique functorial line of ${\mathcal{S}_{\Pi}}$ that is invisible to the adjoint sector ${\mathrm{Sym}}^{2}({\mathcal{S}_{\Pi}}) \simeq {\mathrm{ad}_{\mathbb{C}}}(P_{\Pi})$, and it is the carrier of the abelian electroweak weight; the projected Yukawa sector is therefore the determinant-line sector of the admissible spinor functorial closure, not an external bundle datum. Second, on the gauge-singlet generation triplet ${\mathbb{C}^{3}_{\mathrm{gen}}} = \mathrm{span}(e_{0}, e_{+}, e_{-})$ the squared projective residue takes the closed normal form ${E_{\Pi}}^{2}|_{{\mathbb{C}^{3}_{\mathrm{gen}}}} = {\operatorname{diag}}(1, \tfrac12 + u, \tfrac12 - u)$ of the Schur reduction (PRS), whose exit deficits $\{0, \tfrac12 - u, \tfrac12 + u\}$ order the three generation levels (Q14). The single split coefficient $u$ fixes the dimensionless level structure but not the absolute scale: the projected Yukawa operator, its norm, the sign of $u$, and the complex mixing phase remain downstream open data, so no mass value is claimed. All representation-theoretic and spectral identities are verified by exact symbolic computation, with no sampling.