63维Borsuk问题的一个AI生成反例
An AI Generated Counterexample to Borsuk Problem in Dimension 63
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中文总结 AI 辅助
该研究由ChatGPT利用GPT 5.6 Sol构造出63维含321个点的集合，证明b(63)≥65，为Borsuk问题提供了AI生成的反例。
中文摘要 AI 辅助
我们在R^63中构造了一个包含321个点的集合，该集合无法被划分为64个直径更小的子集，从而证明b(63)≥65。研究从G₂(4)欧几里得表示和63维下的Jenrich-Brouwer 320点核心出发，添加一个经投影和缩放的点，同时保留相关团阻塞结构。该示例及证明完全由ChatGPT使用GPT 5.6 Sol生成，作者已亲自验证结果并承担验证责任，但未对构造的原创性提出主张。
英文摘要
We construct a 321 point set in R^63 that cannot be partitioned into 64 subsets of smaller diameter, proving b(63)>=65. Starting from the G_2(4) Euclidean representation and the Jenrich Brouwer 320 point core in dimension 63, we add one projected and rescaled point while preserving the relevant clique obstruction. The example and proof were generated entirely by ChatGPT using GPT 5.6 Sol. The author has personally verified the result and assumes responsibility for that verification, but claims no credit for the originality of the construction.
