Heat-Flow PDE Hierarchy on Jensen Invariants, Nodal-Curvature Zero Velocity, and Conditional Saddle Perturbation under De Bruijn-Newman Evolution

Analyzes the De Bruijn-Newman deformation Xi_tau(z) = 8 H_tau(2z) (tau = t_DBN, d_tau Xi_tau = -(1/4) d_z^2 Xi_tau) and canonical transverse Wronskian W_tau(d,t) = 16 int_0^inf y sinh(2dy) I_tau(y,t) dy. Relates the Csordas-Smith-Varga and Rodgers-Tao velocity gamma_k'(0) = Xi''(gamma_k)/(4 Xi'(gamma_k)) to the parabolic curvature of R(d,t) = 0; establishes the mirror Gaussian Wigner factorization together with the boundary zero G_{0,tau}(i*eta) = 0 at 2*eta_0 < pi/4 and the conditional numerator inequality for pitchfork saddle perturbation; and proves the second-order radial wave-heat PDE for W_tau/d and the exact heat-flow PDE hierarchy (d_tau + 1/8 d_t^2) L_m(Xi_tau; t) = ((m+1)(2m+1)/4) L_{m+1}(Xi_tau; t) on all Jensen invariants, yielding the (m-1)^2/2 multiple-zero coalescence lift and conditional Lehmer-pair scaling.