Snake-in-the-box updates

On July 16, 2026, A Census of New Snake-in-the-Box Records was submitted to arXiv; this paper introduced new record-length snakes in dimensions 9-13, coils in dimensions 9-12, and symmetric coils in dimensions 10 and 11.

In the weeks since, Ace and I have each used local methods to extend these results further. Given the rapid pace of developments and minimal changes to methodology, I am aggregating these results on this webpage to keep a chronological log. For latest results, I recommend Ace's Snake-in-the-Box lower bounds.

Updates

July 17, 2026 · Ace: 13-d snake: 2922→2928; 11-d coil: 732→734; Ace informed me of the arXiv paper along with these two extensions.
July 22, 2026 · Echols: 13-d snake: 2924→2932; 11-d coil: 732→736; 12-d coil: 1466→1468; I was working over ssh and had not loaded Ace's latest results.
July 23, 2026 · Ace: 11-d coil: 736→738
July 23, 2026 · Echols: 11-d coil: 738→740
August 11, 2026 · Ace: 11-d snake: 746→747
August 13, 2026 · Echols: 13-d coil: 2916→2926; 11-d symmetric coil: 726→730; 13-d symmetric coil: 2810→2822; Found by augmenting my approach with a neutral move from Ace.

Last updated August 13, 2026