指出一篇论文中关键定理的错误，并说明其定义缺陷导致核心结论失效。
Remarks on a recent preprint of Chernikov and Towsner
- 提出反例推翻原定理，揭示证明存在漏洞。
- 指出修改后的定理仍因定义问题而无法成立。
- 适合关注逻辑严谨性与理论连接性的研究者参考。
本文首先针对Chernikov和Towsner在arXiv:2510.02420(1)中的一条定理给出反例。在arXiv:2510.02420(2)中，该定理虽被修改，但如本文所指出，其证明仍存在错误。由于定理的表述变化源于底层定义的调整，这一变化影响了论文的核心主张。由于原定理曾用于建立其工作与Coregliano-Malliaris高阶PAC学习研究之间的联系，而该联系现已消失，因此本文还解释了其定义缺失了我们工作中着力处理的关键要素。
原文摘要 · Abstract (English)
In this brief note, we first give a counterexample to a theorem in Chernikov and Towsner, arXiv:2510.02420(1). In arXiv:2510.02420(2), the theorem has changed but as we explain the proof has a mistake. The change in the statement, due to changes in the underlying definition, affects the paper's claims. Since that theorem had been relevant to connecting the work of their paper to Coregliano-Malliaris high-arity PAC learning, a connection which now disappears, we also explain why their definitions miss crucial aspects that our work was designed to grapple with.
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