All-Orders Olver Protection of the Asymptotic Evans Depth

Research Note 31 in the "Geometry of the Critical Line" programme. This note proves that the asymptotic Evans depth coefficient D_m^(∞) = π|Im(r₁−r₂)|/L is protected against the entire perturbative Olver/Bessel asymptotic series at the endpoints, not merely against its first term (RN29–30). The mechanism is structural: the Olver coefficients a_k(ν) = P_k(ν²) are polynomials in ν² with real coefficients. Since the left-endpoint Bessel order is ν̄ (the complex conjugate of the right-endpoint order ν), the identity a_k(ν̄) = conj(a_k(ν)) holds at every order. The imaginary parts of the endpoint corrections therefore cancel exactly in the Evans depth balance at every perturbative order. Consequently, the finite-λ drift D_m(x) − D_m^(∞) cannot be recovered from endpoint asymptotics alone. It is a genuinely global quantity depending on the full interior solution. The observed c₄ ≈ 17.95 is a well-defined observable but not a local endpoint quantity. This closes the perturbative endpoint-refinement arc. 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 + eiπ − 1/Φ = 0.