Research note demonstrates projective convergence of the SCT transport ratio in a numeric scheme, indicating geometric properties of the critical line.
Research Note 16 in the "Geometry of the Critical Line" programme. Paper 44 established asymptotic proportionality between M₁₁ and M₂₁ in the open chiral SCT connection matrix. This note studies the projective residual Q̃ := R(λ,m) − ρ(m) and shows that it approaches zero along a numerically fitted complex ray with sector angle θ(m) in the present extraction scheme. The convergence is ray-locked rather than spiral or wobbling in the tested window. A candidate angular law θ(m) ∼ π − arg(r₁ − r₂) is tested and found to match to within 0.03 radians for m ≥ 4. No arithmetic interpretation is claimed. Part of a 46-paper open-access programme on the geometry of the Riemann zeta function's critical line. The programme does not claim to prove the Riemann Hypothesis.
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Pavel Kramarenko-Byrd (2026) studied this question.
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