NeuralCert: certified computational discovery of extremal mathematical constructions

NeuralCert presents a framework that learns high‑dimensional variational trial functions in a compact separable form, then spectrally diagnoses, prunes, and exactly certifies them via multimodular evaluation. The method is fully explicit and independently verifiable, and can run on a standard personal computer. Applied to three extremal problems, it demonstrates that neural optimization can discover better constructions, reveal empirical invariants useful for proofs, and expose optimization barriers that inspire new analytic or numerical approaches.

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