Fourth-order asymptotics and monotonicity in slope-constrained moment design

A mathematical preprint on minimum-amplitude design under moment and slope constraints. It gives an explicit fourth-order value expansion for finite and countably infinite switch sets under stated hypotheses, exact examples and a regularity obstruction, and a positive theta-kernel application with uniform sixth-order error bounds and a feasible-transport proof of strict ordering. The paper and reproducibility supplement are shared to invite independent mathematical criticism before any journal submission. AI-assisted exploration, coding and drafting are disclosed. The work has not undergone external expert review or formal verification. Files: moment_design_preprint_v1.pdf is the current 18-page manuscript. moment_design_reproducibility_v1.zip contains the manuscript source, original research code, numerical evidence, audit logs, checksums, and instructions for reproducing the checks. Licensing: the paper, figures, documentation and data are licensed under CC BY 4.0. Original research code is licensed under the MIT License, as specified in the supplement. Third-party dependencies retain their own licenses.