HEXAGONbeta

A contact and coefficient correction for Korenblum's constant

Primarily AI-generated textHuman understanding: some partsmath.CV — Complex Variables

Contributed by Ricardo Pinho

Version 2 / Oct 31, 2026 / CC BY 4.0

Abstract

We give an unrefereed computer-assisted proof that Korenblum's constant in unweighted Bergman space satisfies C68≥0.44685C_{68}\ge 0.44685. The new input retains the signed first contact harmonic in an annular coefficient estimate. An outer factor and square completion yield a correction of 19/20019/200 to the linear coefficient, replacing the 7/1007/100 correction of version 2. A rational measure verifies the resulting moment conditions. We include the analytic argument and describe the finite interval certificates and both infinite tails. The Green/flux input is V. Patankar's (PR 274); the coefficient and moment methods build on Wang, Pinho's earlier construction, and Wikström. There has been no independent human review or formalization.

Provenance statement

Analysis and proof drafting by AI agents under my direction; I reviewed the results at summary level. AI agents also prepared certificates, checking software, and publication materials. No line-by-line human verification is claimed. AI is not an author.

References

  1. D. Niedbala Giraudin, Korenblum flux and enclosing estimates, PR 274; https://github.com/teorth/optimizationproblems/pull/274.link
  2. C. Wang, Domination in the Bergman space and Korenblum's constant, Integral Equations and Operator Theory 61 (2008), 423--432, https://doi.org/10.1007/s00020-008-1587-4; A lower bound on Korenblum's constant, Proceedings of the American Mathematical Society 153 (2025), 1209--1214, https://doi.org/10.1090/proc/17112.DOI
  3. F. Wikström, Moment duality and an improved lower bound for Korenblum's constant, Lemma 3.1 (moment integration); https://arxiv.org/abs/2607.17748.link
  4. R. Pinho, earlier covering-strip coefficient construction and references to Wang and Schuster; https://github.com/rpinho/korenblum-c68-certificate.link
  5. R. Pinho, Korenblum C68 certificate , contact-spectral , commit a8bfa25 ; https://github.com/rpinho/korenblum-c68-certificate/tree/a8bfa25da9b07f0a7b8fefcd5043c0547855c9d1/contact-spectral.link

Version history

  1. v1Submitted by Ricardo PinhoInitial depositSupersededOct 30, 2026
  2. v2Submitted by Ricardo PinhoSubmitted as a new versionSupersededOct 31, 2026
  3. v3Submitted by Ricardo PinhoSubmitted as a new versionCurrentNov 03, 2026