The Constrained Jet of the Lorentzian Eliminated Block and the Chiral Generator: From the Schur Reduction to the Transported Equivariance Defect

This note isolates a single operator-level lemma in the fermionic-matter sub-programme of Cosmochrony, logically between the Schur reduction of the projective residue and the physical identification of the chiral generator. The Schur reduction writes the projective endomorphism as E_{} = -ₒ\, D\, (1-P) \, D\, ₒ^*, exhibiting the eliminated block 1-P as the controlling object of the three-generation split coefficient u; the companion genus analysis fixes the electric sign _{^2} < 0, while the absolute value |u|, the Yukawa sector, and the mass spectrum are kept downstream. We freeze the structural form that the Lorentzian eliminated block must take. Writing the self-adjoint projector family as a jet 1-P (s) = Q₀ + s Q₁ + s² Q₂ + O (s³) along the J_{}-odd modulus s, the projector constraints force Q₁ to be a purely off-diagonal Grassmann tangent, Q₁ = A, Q₀ with Q₀ Q₁ Q₀ = 0 = (1-Q₀) Q₁ (1-Q₀), and pin the diagonal blocks of Q₂ to Q₁² with opposite signs. Decomposing the generator by J_{}-parity, A = A_+ + A_-, only the chiral part contributes to the split: {₉_{-odd}} Q₁ = A_-, Q₀. Propagation through the J_{}-even pair (ₒ, D) grades the residue jet as E₀ even, E₁ odd, E₂ even, so the J_{}-odd part of E_{}² at first order is the anticommutator \E₀, E₁\, and the split source is u (s) = s\, J₃, \E₀, E₁\ / J₃, J₃ + O (s³). With phase-free jet data the mixing coefficient v vanishes identically while u is generically non-zero, so u 0 is structurally admissible with no R₌₈ₗ leakage and with |u| left entirely free. We then identify the split-sourcing component of the generator. Because the antiunitary Born–Infeld parity exchanges chiralities, the J_{}-odd part of the eliminated block has chiral-diagonal component equal to the transported equivariance defect _{} (P) = ₋₋ - \, ₑₑ\, ^-1 of, so {₉_{-odd}} (1-P) ₋₋ = 12 _{} (P) and, along the modulus, {₉_{-odd}} Q (0) ₋₋ = 12 ₛ _{} (0). The chiral generator A_- is therefore not a new selector but exactly the infinitesimal transported chiral defect rate; its absolute value is not normalised here. All identities are verified by exact symbolic and exact-rational computation, leaving a single downstream target — the admissible normalisation of ₛ _{} (P) |₀ — with no circularity against |u|, the chiral-frontier normalisation, or the Yukawa sector.