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The aim is to develop a higher-order theory for sum-integral comparisons based on curvature and kernel structures.

April 28, 2026Open Access

Curvature and Kernel Structure in Sum–Integral Comparison: A Higher-Order Theory

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The aim is to develop a higher-order theory for sum-integral comparisons based on curvature and kernel structures.
Formalization of results in Lean 4 using mathlib.
Derivation of exact kernel representation for even-order functionals.
Proof of explicit nonnegative kernel mass constants C_m.
Exact Peano-kernel representations for even-order functionals established.
Nonnegative kernels K₂m verified for systematic quadrature errors.
Structural distinctions between even-order and odd-order kernel cases demonstrated.

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This randomized trial establishes kernel representations for even-order functionals, suggesting a new framework for quadrature errors.

Bob Jefferson (2026) studied this question.

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