A computer-assisted sharp diagonal Hlawka inequality for real exponents p ≥ 21
Year: 2026
Type: preprint
Abstract: We give a computer-assisted proof that, for every real p ≥ 21, the dimension-independent sharp Hlawka constant of complex ℓ_p is the maximum of an explicit one-parameter ratio on the cyclic triple (-t,1,1), (1,-t,1), (1,1,-t), 1/2 ≤ t ≤ 2. The new finite calculation covers 21 ≤ p ≤ 32; the range p ≥ 32 uses a previously accepted Prove2Me theorem. The improvement uses norm caps, clipped pair-coordinate tails, and linear coordinate-sum constraints on a convex averaging domain, together with a sharper residual Hessian estimate. Rational linear-programming dual witnesses and interval certificates cover real exponent intervals, rather than sampled exponents. The finite obligations pass both Arb and a standard-library dyadic rational implementation. We give the analytic reduction, certificate specification, and reproduction instructions. An accompanying Lean formalization of the original uniform complex least-constant goal is verified on Prove2Me with no open dependencies, reusing the accepted p ≥ 32 tail. Independent analytic review remains pending, and no optimality of the exponent threshold 21 is asserted.
Author: Xu, Yuxuan
Institution: Wuhan University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222886706
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