Theoretical analysis reveals determinant-line Yukawa projections and generation exit deficits in a spinor bundle model, indicating an intrinsic structural ordering for fermion families.
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 SΠ produced by the Lorentzian complexification of the metaplectic Weil carrier of Q14, the determinant line LY:= ²(SΠ) is the unique functorial line of SΠ that is invisible to the adjoint sector Sym²(SΠ) adC(PΠ), 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 C³gen = span(e₀, e₊, e₋) the squared projective residue takes the closed normal form EΠ²|_C³gen = diag(1, 12 + u, 12 - u) of the Schur reduction (PRS), whose exit deficits \0, 12 - u, 12 + 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.
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Jérôme Beau (2026) studied this question.
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