Paper 46 in the "Geometry of the Critical Line" programme. This paper derives the leading asymptotic law for the Evans zeros of the connection-matrix entry M₂₁ (λ, m) of the chiral SCT operator. The proof uses exact Liouville reduction (the identity B = −A'/2), endpoint Laurent analysis, and complex-order Bessel matching. The Evans numerator reduces to sinh (β + iα), where β = Im (ν) π and α = Φₜot − Re (ν) π − π/2. The main results at leading asymptotic order: (i) the leading asymptotic Evans model has no real zeros for m ≠ 0; (ii) the zeros satisfy Δ√ (Re λₙ) → π/L with L = 2/k; (iii) for m > 0 the zeros lie in Im (λ) 0 by chiral conjugation. Numerical verification in the m = 2 and m = 4 sectors confirms the predicted depth to within 1% and 4% respectively, with the discrepancy consistent with finite-λ convergence. Subleading corrections are not computed here. The lower-half-plane location is a leading-order result, not yet a full non-perturbative theorem. No arithmetic interpretation is claimed. Part of a 46-paper open-access programme on the geometry of the Riemann zeta function's critical line, anchored by the SCT 5-Manifold and the cover equation Φ + e^iπ − 1/Φ = 0.
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Pavel Kramarenko-Byrd
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Pavel Kramarenko-Byrd (Sun,) studied this question.
www.synapsesocial.com/papers/69ccb76c16edfba7beb89619 — DOI: https://doi.org/10.5281/zenodo.19323384