Claims

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2026_04_22_bae: Bae proves H(k)^{1/k}/k tends to infinity, with the explicit rate H(k)^{1/k}/k at least (1/e - o(1)) k / log k, answering the displayed question; the site's curator records it as a solution.

2026_06_01_fox_hunter: Fox and Hunter prove H(k) is at least k^{(1-o(1)) k log k}, the strongest known lower bound, from their many-color van der Waerden bound; it answers the displayed question independently of Bae.

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