Exact Whittaker Reduction and the Anti-Stokes Obstruction for the SCT Transport Ratio

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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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-05-12
DOI
https://doi.org/10.5281/zenodo.19316361
Primary Topic
Fluid dynamics and aerodynamics studies
Type
preprint
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preprint

Exact Whittaker Reduction and the Anti-Stokes Obstruction for the SCT Transport Ratio

Pavel Kramarenko-Byrd
Zenodo (CERN European Organization for Nuclear Research)
Fluid dynamics and aerodynamics studies
preprint

Exact Whittaker Reduction and the Anti-Stokes Obstruction for the SCT Transport Ratio

Pavel Kramarenko-Byrd
preprint en

Abstract

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.

Zenodo (CERN European Organization for Nuclear Research)
Affordable and clean energy
Fluid dynamics and aerodynamics studies
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Exact Whittaker Reduction and the Anti-Stokes Obstruction for the SCT Transport Ratio — Pavel Kramarenko-Byrd · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS