AI 中文总结
本注针对三维欧拉奇点计算机辅助证明，澄清非局部误差与剖面残差误差的区别，并指出相关文献的证据无法否定已有残差估计，也不支持角增长假设在Hou-Luo场景下的适用性。
AI 中文摘要
在文献[zhang2025dimension]中，作者讨论了自相似剖面的不存在性结果在Hou-Luo场景下的适用性，并对文献[ChenHou2023a,ChenHou2023b]中构造的近似自相似剖面提出了疑问。在本注中，我们澄清两个要点：第一，文献[zhang2025dimension]中识别的远场偏差是原始非局部泊松误差，而非文献[ChenHou2023a,ChenHou2023b]稳定性证明中使用的剖面残差误差；剖面残差中相关的非局部贡献包含非局部速度误差乘以额外的衰减因子，这些衰减因子为远场估计提供了关键的小性条件。第二，我们检验了文献[zhang2025dimension][注2.4]中用于支持其[命题2.3(i)]假设适用性的基于图的证据，结果显示相同的网格点数据并不支持该解释。因此，文献[zhang2025dimension]中的比较和基于图的证据既未否定文献[ChenHou2023a,ChenHou2023b]中的残差估计，也未证明所声称的角增长假设在Hou-Luo场景下的适用性。
英文摘要
In \cite{zhang2025dimension}, the author discusses the applicability of a nonexistence result for self-similar profiles to the Hou--Luo scenario and raises questions about the approximate self-similar profile constructed in \cite{ChenHou2023a,ChenHou2023b}. In this note, we clarify two main points. First, the far-field discrepancy identified in \cite{zhang2025dimension} is the raw nonlocal Poisson error, not the profile residual error used in the stability proof of \cite{ChenHou2023a,ChenHou2023b}. The relevant nonlocal contribution to the profile residual contains the nonlocal velocity error multiplied by additional decaying factors, which provide crucial smallness in the far field estimates. Second, we examine the figure-based evidence used in \cite[Remark 2.4]{zhang2025dimension} to support the applicability of the assumption in \cite[Proposition 2.3(i)]{zhang2025dimension}, and show that the same grid-point data do not support that interpretation. Thus the comparisons and figure-based evidence in \cite{zhang2025dimension} neither invalidate the residual estimates in \cite{ChenHou2023a,ChenHou2023b} nor justify the claimed applicability of the angular-increase assumption to the Hou--Luo scenario.
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