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The aim is to validate strict positivity and inequalities for an order-10 operator chain on a defined interval.

August 2, 2026Open Access

Directed Computer-Assisted Certification of a Local Order-10 Operator-Chain Corridor on the Real Interval 5 ≤ s ≤ 14.25 via a Fixed Uniform b₁ Remainder Coefficient, Proof-Preserving Critical-Block Adaptation, and Panel-Aligned Derivative-Group Enclosures

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The aim is to validate strict positivity and inequalities for an order-10 operator chain on a defined interval.
Directed adaptation of critical panel width to maintain operator properties.
Recomputation of specific blocks while inheriting verified properties from previous slabs.
Implementation of fast dual accumulation for verification of derived coefficients.
All 128 final fixed coefficient substitutions are positive.
The derived inequalities Q_(10,10)^+(s) > 0 and W_10(s) > 0 are established across the interval.
Recomputing certain parameters achieves passage of critical verification gates.

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Preprint update certifies positivity inequalities in a local operator chain, indicating new methodological advancements.

Alexanja Senke (2026) studied this question.

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