标题： 决策问题在奇数大小字母表中的相变 显示英文标题

标题： Phase Transitions in Decision Problems Over Odd-Sized Alphabets

摘要： 在[A. Jackson, 解释偶数大小字母表上决策问题中相变的普遍性(2025), arXiv:2501.14569]中，我证明了在偶数大小字母表上的大量决策问题中总是存在相变，部分解释了为什么相变在决策问题中如此常见。 然而，奇数大小字母表上的决策问题没有被讨论。 在这里，我纠正了这一疏漏，展示了奇数大小字母表上类似的决策问题子集也总是表现出相变。 显示英文摘要

摘要： In [A. Jackson, Explaining the ubiquity of phase transitions in decision problems (2025), arXiv:2501.14569], I established that phase transitions are always present in a large subset of decision problems over even-sized alphabets, explaining -- in part -- why phase transitions are seen so often in decision problems. However, decision problems over odd-sized alphabets were not discussed. Here, I correct that oversight, showing that a similar subset of decision problems over odd-sized alphabets also always exhibit phase transitions.