Non-Canonicity of the Subleading Depth Drift and Structural Closure of the Evans Arc

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Authors: Pavel Kramarenko-Byrd
Cited by: 8

Abstract

Research Note 32 in the "Geometry of the Critical Line" programme. This note establishes numerically that the Evans asymptotic arc terminates at leading order not by convenience but by structure. The Riccati remainder functional R_m(λ) = ∫ [P_exact − P_WKB] dδ is examined at multiple endpoint cutoffs η. Three results: (1) the real part Re(R_m) stabilises as η → 0, providing numerical evidence for an η-independent global phase defect in the spacing sector; (2) the imaginary part Im(R_m) diverges logarithmically in η and is therefore not matching-invariant; (3) consequently, the subleading depth drift c_m/√x is a scheme-dependent global matching quantity and does not admit a canonical analytic representative within the present Evans/endpoint-interior formulation. The leading depth law D_m^(∞) = π|Im(r₁−r₂)|/L is, within the present Evans/endpoint-interior formulation, the last theorem-grade invariant identified in this arc. The Evans asymptotic arc is complete within the present endpoint/interior formulation. Any future reopening requires a genuinely new framework (trace formula, Fredholm determinant, or equivalent). 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.

Fields of Study & Subjects

Numerical methods in engineering Groundwater flow and contamination studies High-pressure geophysics and materials

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
29 March 2026
Language
EN
Document type
Preprint