On an Essential Unverified Step in Baek's "Optimality of Gerver's Sofa" and three ancillary corrections to arXiv:2411.19826v1

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-19
DOI
https://doi.org/10.5281/zenodo.22839657
Primary Topic
Relativity and Gravitational Theory
Type
preprint
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preprint

On an Essential Unverified Step in Baek's "Optimality of Gerver's Sofa" and three ancillary corrections to arXiv:2411.19826v1

Zeraoulia Rafik
Zenodo (CERN European Organization for Nuclear Research)
Relativity and Gravitational Theory
preprint

On an Essential Unverified Step in Baek's "Optimality of Gerver's Sofa" and three ancillary corrections to arXiv:2411.19826v1

Zeraoulia Rafik
preprint en

Abstract

Baek's preprint "Optimality of Gerver's Sofa" (arXiv:2411.19826v1) claims that Gerver's sofa attains the maximal area in the moving-sofa problem. This note isolates a proof-completeness issue already acknowledged locally by Baek and shows that it enters the final argument in two logically distinct ways. Theorem 8.4.1 identifies the formal Gerver-Romik curves with the actual support/contact curves and niche boundary of Gerver's sofa, while Remark 8.4.1 states that these geometric assertions still require rigorous logical/symbolic verification. Parts of Theorem 8.4.1 feed through Theorem 8.4.3, Proposition 8.4.4, and Theorem 8.4.5 into the directional-derivative argument culminating in Corollary 8.5.8; independently, the niche-boundary assertion in Theorem 8.4.1 is used directly in Theorem 8.4.6 to identify A(K)=Q(K,B_K,D_K)=|G|. Both ingredients are invoked in the final proof of Theorem 1.1.1. Thus the public v1 proof is incomplete as written unless the verification of Theorem 8.4.1 is supplied. The note also isolates an internal attribution mismatch in Theorem 6.1.2 concerning Gerver's Theorem 2 and the stronger notion of globally maximizing polygon caps. Finally, it corrects the bounded-density formulation in Proposition 5.1.4 and two sign/index errors in Theorem 8.5.7. None of these observations proves that Gerver's sofa is non-optimal; they concern the completeness and internal consistency of the written proof.

Zenodo (CERN European Organization for Nuclear Research)
Université Djilali Bounaama Khemis Miliana (DZ)
Relativity and Gravitational Theory
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