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 Rₘ (λ) = ∫ Pₑxact − PWKB dδ is examined at multiple endpoint cutoffs η. Three results: (1) the real part Re (Rₘ) stabilises as η → 0, providing numerical evidence for an η-independent global phase defect in the spacing sector; (2) the imaginary part Im (Rₘ) diverges logarithmically in η and is therefore not matching-invariant; (3) consequently, the subleading depth drift cₘ/√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 Dₘ^ (∞) = 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.
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Pavel Kramarenko-Byrd
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Pavel Kramarenko-Byrd (Sun,) studied this question.
www.synapsesocial.com/papers/69ccb63f16edfba7beb87e3c — DOI: https://doi.org/10.5281/zenodo.19323394
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