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.

Mods, please delete this entry, I succeeded in posting it in a better way: https://news.ycombinator.com/item?id=47290805

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.

In February 2022, Don Knuth found a cool graph which contains all 4-vertex graphs as subgraphs. Furthermore, they can be visited in revolving-door Gray code order.

He reported about it in exercise 291 in pre-fasicle 7a, and asked if someone could make an animated video of it. This is my attempt at it.

Any remarks or suggestions for improvement are welcome.

Fantastic. The audio (as suggested by Knuth) is a nice touch. If people don't like it, they can easily mute.

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).

suggestion: remove the audio.

Why? I understood the audio to be proof that it is a Gray code?

Or turn on mute.