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This work aims to develop a formal framework for sum-integral comparison using curvature representations.

April 12, 2026Open Access

Curvature and Kernel Structure in Sum–Integral Comparison: II. Non-Uniform Partitions and Scaled Bounds

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This work aims to develop a formal framework for sum-integral comparison using curvature representations.
Formalization based on curvature representations in Lean 4.
Used non-uniform partitions for accurate sum-integral estimation.
Derived local bounds representing cubic scaling of errors across partitions. Justification of error through inequality framework.
Established cubic scaling of trapezoidal error with interval length.
Developed a non-uniform quadrature theorem with precise bounds.
Formalized results verified within the Lean 4 framework.

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This formalization provides non-asymptotic bounds for sum–integral comparisons, highlighting geometric aspects of quadrature error.

Bob Jefferson (2026) studied this question.

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