AI-based mathematical research from a selected corpus: results in statistical validation and optimization

This collection presents AI-based mathematical research starting from a selected corpus connecting mathematical finance, statistical validation, numerical optimization, and optimization under uncertainty. A concise overview describes the research principles, principal results, and identified counterexamples and corrections. Five complete research articles follow as Appendices A–E: A. Universality, finite-sample calibration, and dependent sampling for nearest-neighbour memorization ratios. B. Error budgets, attainable selection, and convergence rates for noisy radial-basis optimization. C. Fixed-grid Svensson fitting: complete boundary geometry, exact interpolation, and certified global approximation. D. Certified approximations and stability of entire robust regret fronts. E. Stability and sharp sampling rates of entire robust regret fronts. Contributions include finite-sample universality classifications, dependence counterexamples and repairs, quantitative exploration bounds, exact interpolation and nonattainment thresholds, corrected robust regret certificates, and sharp distinctions between convergence rates of entire decision fronts and their objective images. The research was conducted using AI under human direction. The articles provide mathematical proofs, explicit assumptions, references, and limitations. Counterexamples distinguish proposed extensions from published assertions and identify the precise conclusions affected. The collection is presented as a preprint and does not claim external peer review. The single PDF contains 139 pages, including the overview and all five articles, with navigation bookmarks and individual article pagination.