| Upper bounds |
| 43,948,808 | Egan's bound, Greg Egan, 2018 | Paper |
| 43,948,807 | Egan's bound minus one, Uku Raudvere, 2026 | Lean, kernel-checked |
| 43,942,416 | The 101/120 bound, Jay Pantone jaypantone, 2026 | Lean, kernel-checked |
| 43,932,672 | The 3/5 bound, Jay Pantone jaypantone, 2026 | Lean, kernel-checked |
| 43,930,548 | W-0079, the shortest known word, Jay Pantone jaypantone, 2026 | Checked word |
| 12,645 | gap |
| Lower bounds |
| 43,917,903 | S(11) ≥ 43,917,903, Jakub Halfar, 2026 | Lean, kernel-checked |
| 43,917,903 | Pantone's bound, Jay Pantone jaypantone, 2026 | Lean, statement reviewed |
| 43,917,793 | Halfar's general bound, Jakub Halfar, 2026 | Lean, statement reviewed |
| 43,916,736 | Kisic's bound, Marin Kisic and Jakub Halfar, 2026 | Lean, kernel-checked |
| 43,916,235 | Liu's bound, Xiaolong Liu, 2026 | Lean, statement reviewed |
| 43,912,566 | The Hunter–Raudvere bound, Zach Hunter and Uku Raudvere, 2026 | Lean, statement reviewed |
| 43,910,408 | Raudvere's bound, Uku Raudvere, 2026 | Lean, kernel-checked |
| 43,908,489 | 4chan + 1, Robin Houston, 2018 | Lean proof |
| 43,908,488 | The 4chan bound, Anonymous 4chan poster, Robin Houston, Jay Pantone jaypantone and Vince Vatter, 2011 | Paper |