Primitive sequences obtained from iterated antiderivatives of the CDF are homeomorphic to probability measures on compact intervals, equivalent to factorial-rescaled moments of the reflected variable, and yield sharp bounds on functionals when the first m terms are fixed.
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Five improved inequalities were found with AI help: better Gaussian perimeter bounds for convex sets, sharper L2-L1 moments on the Hamming cube, a strengthened autoconvolution inequality, improved g-Sidon set bounds, and an optimal balanced Szarek inequality.
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Primitive Sequences for Probability Measures on Compact Intervals
Primitive sequences obtained from iterated antiderivatives of the CDF are homeomorphic to probability measures on compact intervals, equivalent to factorial-rescaled moments of the reflected variable, and yield sharp bounds on functionals when the first m terms are fixed.
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Grokability in five inequalities
Five improved inequalities were found with AI help: better Gaussian perimeter bounds for convex sets, sharper L2-L1 moments on the Hamming cube, a strengthened autoconvolution inequality, improved g-Sidon set bounds, and an optimal balanced Szarek inequality.