AI 中文总结
该研究针对双接收者广播信道，借助GPT-5.6 Sol构造两个反例，证明Gohari等人提出的马尔可夫性猜想不成立，给出了非马尔可夫构造的目标值更优的结果。
AI 中文摘要
我们给出了Gohari、Liu和Nair（ISIT 2025）提出的马尔可夫性猜想的两个反例，该猜想是关于Marton内界相关对偶泛函最优解的结构性猜想，若成立将极大简化Marton内界的评估。两个反例均为三元输入广播信道，具有严格正的转移概率，采用相同的非矩形2×2辅助结构。对每个反例，我们给出了明确的非马尔可夫构造，其目标值严格大于任何满足所猜想马尔可夫结构的构造所能达到的值。两个例子均借助GPT-5.6 Sol得到，证明了马尔可夫性猜想不成立。
英文摘要
We present two counterexamples to the \emph{Markovity Conjecture} of Gohari, Liu and Nair (ISIT 2025), which is a structural conjecture concerning the optimizers of the dual functional associated with Marton's inner bound and, if true, would greatly simplify the evaluation of Marton's inner bound. Both counterexamples are ternary-input broadcast channels with strictly positive transition probabilities and use the same nonrectangular $2\times2$ auxiliary structure. In each case, we exhibit an explicit non-Markov construction whose objective value is rigorously larger than that achievable by any construction satisfying the conjectured Markov structure. Both examples are obtained with the assistance of GPT-5.6 Sol and disprove the Markovity Conjecture.
