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 EΠ = -ΠS\,D\,(1-P)\,D\,ΠS*, 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 μχ² < 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 JΠ-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 JΠ-parity, A = A₊ + A₋, only the chiral part contributes to the split: Π_JΠ-odd Q₁ = [A₋, Q₀]. Propagation through the JΠ-even pair (ΠS, D) grades the residue jet as E₀ even, E₁ odd, E₂ even, so the JΠ-odd part of EΠ² at first order is the anticommutator ₀, E₁\, and the split source is u(s) = s\, J₃, ₀, 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 Rₘᵢₓ 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 JΠ-odd part of the eliminated block has chiral-diagonal component equal to the transported equivariance defect Δχ(P) = πLL - τ\,πRR\,τ⁻¹ of, so [Π_JΠ-odd(1-P)]LL = 12 Δχ(P) and, along the modulus, [Π_JΠ-odd Q(0)]LL = 12 ∂ₛ Δχ(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 Δχ(P)|₀ — with no circularity against $|u|$, the chiral-frontier normalisation, or the Yukawa sector.