Second-Order De Branges-Nevanlinna Kernels, Derivative-Wronskian Splitting, Davenport-Heilbronn Blind Spots, and the Differential Threshold beta*
Year: 2026
Type: preprint
Abstract: Studies the second-order differential structure function E_{alpha,beta}(z) := F(z) - i*alpha*F'(z) - beta*F''(z) and its de Branges-Nevanlinna Hermitian kernel K_{alpha,beta}(z_1, z_2). Proves the exact cross-term-free splitting K_{alpha,beta}(t-id, t-id) == (alpha/pi)*W_tilde_{0,1}(d,t) + (alpha*beta/pi)*W_tilde_{1,2}(d,t), critical-line Lehmer near-coalescence lifting at order d^0, the radial 4D-Laplace PDE and canonical Wigner operator I^{(1)}(y,t) = (y^2 + (1/4)*d_t^2)*I(y,t) with (1/40)*(ln(t/2pi))^5 diagonal and O(t^{-5/2}) horizon-pair scaling, and order-M Hurwitz chains. Crucially demonstrates that Hermite-Biehler membership of E_{alpha,beta} for fixed beta > 0 corresponds only to real zeros of F - beta*F'' (strictly weaker than RH), exposing an explicit Davenport-Heilbronn blind spot (beta_coal = 0.04467500, beta_blind = 0.05349534, global beta*(Xi_DH) = +infinity) and motivating the open differential reality threshold beta*(F).
Author: Missiaen, Thijs
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225833373
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