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Knuth updated his 'Claude cycles' note with new spectacular developments. The remaining open problem for even m was completely solved using LLMs, including proofs of correctness. The techniques used are very interesting, including multiple agents working together. See the references of the note for details.

Also note the 'Over and out' section.

Knuth updated his 'Claude cycles' note with new spectacular developments. The remaining open problem was completely solved using LLMs, including proofs of correctness. See the Postpostscript section at the bottom of the note.

Also note the 'Over and out' section.

I made a fun Roundtrip puzzle because it is Pi day today.

Thanks. The original idea by Knuth was to have each vertex have both a separate tune and a separate instrument/timbre, with each combination sounding not too bad.

I couldn't make this sound good with 8 separate instruments, so I went for the next best thing: a single instrument, with each vertex playing one note (0->B, 1->C,...7->a).