Local Maximal-Canard Threshold Shifts under Runge–Kutta Discretization: An Observable-Specific Order Condition

Abstract

This research compendium contains the complete 106-page extended preprint and its compilable LaTeX source, together with exact symbolic checks, numerical programs, machine-readable data, vector figures, environment specification, manifests, and SHA-256 checksums. The preprint proves an actual local map–flow maximal-canard threshold law on compact domains of symmetric two- and three-stage Runge–Kutta families. The threshold functional detects only the chain-tree coordinate of the order-three B-series defect, so class-wide leading-bias cancellation is equivalent to b^T A c = 1/6 while the independent bushy-tree condition may fail. Version 1.3.4 synchronizes the public preprint title with the dynamics-first title of the journal manuscript. The manuscript text, theorem, method domains, asymptotic coefficients, joint wedge, remainders, root tube, applications, and numerical data are unchanged from version 1.3.3. The finite-boundary van der Pol and rational Rosenzweig–MacArthur computations illustrate local fixed-section threshold laws; they do not construct selected invariant manifolds numerically or compute a global periodic-orbit canard explosion. The symbolic programs verify finite identities and do not replace the analytic remainder estimates.