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Research note establishes transformation of endpoint equation to a Whittaker equation, suggesting refined mathematical interpretation.
Research Note 15 in the "Geometry of the Critical Line" programme. Paper 43 showed that the leading high-energy endpoint equation for the SCT connection matrix reduces to a complex-order Bessel equation. This note establishes a stronger result: the corrected endpoint equation, retaining the subleading O(ε⁻¹) potential term, transforms exactly to a Whittaker equation under the substitution z = 2ix, with purely imaginary Coulomb parameter κ = im²/(4k√λ) and complex order μ = ν(m). The Bessel model of Paper 43 is recovered as the κ → 0 limit. However, the standard Whittaker connection formulas do not directly apply on the physical ray arg z = π/2, which lies on an anti-Stokes line. The missing ingredient is the sectorial Stokes connection map for the Whittaker equation on the imaginary axis. No arithmetic interpretation is claimed. Part of a 46-paper open-access programme. 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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