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