Local Lanczos Defects Control the Short-Time Loss of Krylov Speed-Limit Saturation and Its First Correction

This preprint studies the short-time loss of saturation of the Krylov complexity dispersion bound in the zero-diagonal operator-Krylov setting. Writing c_n = b_n² and defining the local third finite-difference defect Ω_r = Δ³c_r, it establishes a hierarchy in which the first nonzero defect determines both the time order and the leading coefficient of the saturation deficit. The first subleading correction is also derived, and the finite-jet result is extended to infinite Jacobi/Krylov chains under an explicit at-most-linear growth assumption on the Lanczos coefficients. Independent research by Valentino Lanzarini, developed with the support of artificial-intelligence tools.