Claims

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2026_04_22_chojecki: A note written with GPT-5.4 Pro proves the coloring for every m at most the continuum's successor and, from large-cardinal hypotheses through Garti and Hayut, a forcing extension in which it fails from some m on.

2026_05_24_wu: Wu observes that a failure of the coloring implies that zero sharp exists, so the answer is yes in L for every m, while Garti and Hayut's forcing from I1 gives a model with a negative instance; the problem is independent.

2026_07_28_white: A working report written with Claude (Anthropic) reproves that a failure of the coloring implies zero sharp, so the answer is yes in L, and that a negative instance is consistent from I1; a least bad cardinal is regular.

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