Length 1156 over {0, 1, 2, 3, 4, 5, 6, 7}

Word of length 1156 over {0, 1, 2, 3, 4, 5, 6, 7}

by Aayush Rajasekaran, 2026-08-26 · JSON

This is a historical record from 2026-08-26, superseded on 2026-08-27 by length 1886 — jump to the current record (2718).

Display: drawn for the equivalent alphabet translated by -3 (drift removed).

2 5 0 1 6 3 7 4 0 2 0 1 2 4 3 0 2 4 6 7 4 3 2 4 7 1 0 2 0 1 0 3 1 6 0 2 1 0 5 7 2 0 2 4 5 7 0 3 7 6 7 4 6 4 1 4 7 4 6 3 0 1 4 0 6 7 0 2 0 4 2 0 2 1 0 6 4 7 5 4 0 6 4 5 3 7 6 5 7 2 6 4 5 7 6 5 3 7 5 6 0 4 1 0 1 5 3 5 7 4 0 2 0 4 0 1 0 2 1 0 1 6 4 1 3 4 2 6 4 7 6 1 7 6 4 6 0 2 0 4 0 1 6 0 3 1 5 7 6 1 2 1 0 4 1 0 2 1 7 1 0 1 2 0 1 0 4 0 2 0 1 0 4 5 7 3 1 3 0 1 5 0 7 2 7 6 7 0 5 6 3 1 2 0 6 3 0 1 0 2 0 1 0 4 2 0 1 0 3 6 5 3 7 0 1 2 4 7 6 2 6 7 5 6 2 0 6 5 6 4 6 3 1 2 0 5 3 5 7 0 3 1 0 2 3 1 0 7 6 7 3 1 6 2 6 0 1 3 2 5 7 6 7 5 4 6 4 1 0 1 2 5 7 6 7 3 7 6 7 5 7 2 7 5 3 1 5 4 6 2 0 1 2 0 2 3 1 7 6 0 3 7 6 7 2 3 1 0 6 7 3 0 1 3 0 2 0 1 0 2 0 4 1 7 4 0 1 6 1 7 6 4 1 7 5 7 6 4 6 7 6 2 0 5 7 6 4 7 1 3 0 2 4 0 3 0 1 5 6 2 1 5 2 0 1 3 0 2 0 1 0 2 0 4 3 5 0 4 2 3 1 0 2 1 6 4 1 0 7 3 5 7 5 6 7 0 1 2 1 7 1 4 0 1 0 2 1 7 0 3 6 7 3 0 2 0 4 6 5 0 2 0 1 0 2 7 0 2 1 0 4 0 1 0 2 0 1 0 3 1 5 1 0 2 0 1 0 3 7 6 2 0 2 5 3 1 0 1 3 1 0 2 0 4 1 4 2 4 6 5 7 3 4 0 1 0 2 0 7 1 0 1 2 0 1 4 7 1 0 2 7 5 2 0 1 6 4 0 2 0 3 1 7 3 7 6 5 3 7 6 2 0 1 0 4 3 4 0 1 7 5 2 0 3 7 0 6 0 2 0 6 0 1 0 4 1 4 3 0 2 7 6 2 6 1 5 7 2 5 7 4 7 5 7 4 3 2 1 2 7 4 0 2 3 4 0 2 0 4 6 1 6 0 1 0 7 2 6 7 5 6 5 2 0 1 3 1 0 2 5 1 5 7 2 0 1 6 4 0 2 0 5 0 1 3 0 1 0 2 0 1 0 3 1 6 3 6 7 5 7 2 4 2 1 0 1 2 1 0 6 4 6 0 5 3 6 7 5 6 4 5 2 3 0 1 3 7 5 4 6 4 0 1 6 1 0 2 0 1 0 4 1 0 1 6 2 7 6 4 1 3 1 0 2 1 3 7 5 2 0 5 3 5 7 6 4 6 7 5 3 5 1 6 4 1 0 3 6 5 7 2 6 5 7 6 3 7 6 7 5 7 6 1 0 6 4 7 6 4 6 2 7 3 0 1 0 2 7 3 0 2 6 3 7 1 7 6 5 6 7 6 3 0 3 7 1 3 2 0 3 5 0 2 0 1 0 4 0 1 2 3 7 2 0 5 3 7 5 0 4 7 4 3 0 1 0 2 1 6 3 2 0 2 1 0 1 3 0 5 1 0 3 1 0 1 2 7 5 1 0 5 6 2 4 6 1 7 5 7 6 2 1 6 5 0 7 0 1 2 3 1 0 2 0 1 0 3 7 5 1 2 0 7 3 7 2 0 7 1 7 2 5 7 6 7 5 7 4 6 7 4 0 3 5 7 6 1 0 4 2 7 2 5 0 1 3 0 2 7 1 2 0 1 3 0 2 0 5 2 7 6 2 0 4 3 5 7 4 6 7 6 2 1 3 1 0 1 5 6 3 0 4 6 7 1 5 2 3 5 7 3 4 7 6 7 5 4 6 0 4 3 7 5 7 6 4 7 6 7 5 7 6 7 2 1 6 4 7 6 3 5 0 2 1 0 7 4 1 2 6 5 2 5 7 5 6 4 5 7 6 7 4 6 0 3 5 4 7 6 2 0 4 5 2 3 0 1 0 3 0 4 1 4 7 6 1 3 0 7 5 7 6 7 0 5 1 5 7 6 1 2 0 4 1 7 4 3 0 1 3 6 0 2 1 0 1 4 1 2 0 2 7 6 1 0 1 2 1 3 7 1 5 7 6 7 5 1 0 3 7 1 7 4 6 7 5 7 6 4 0 4 7 1 6 7 2 1 4 1 0 3 7 5 2 1 0 2 4 0 3 0 1 4 7 4 3 6 0 3 5 7 5 6 1 4 7 6 4 7 2 7 6 5 2 5 3 1 2 0 1 7 1 0 6 4 7 5 7 1 7 5 7 6 5 1 3 4 2 4 3 7 6 7 5 7 6 2 3 7 6 2 7 4 1 0 6 7 6 0 6 3 2 5 7 5 0 2 4 3 7 4 7 0 6 7 3

Alphabet {0, 1, 2, 3, 4, 5, 6, 7}

size 8 · diameter 7 · record length 2718 · JSON

open No exhaustive search has settled this alphabet; the record is a lower bound on the (possibly infinite) maximum.

Know the exact maximum? Log in to claim this alphabet closed.

Record history

2718 (was 2458) — David Renshaw, 2026-09-09
2458 (was 2380) — David Renshaw, 2026-09-04
2380 (was 2245) — David Renshaw, 2026-08-28
2245 (was 1886) — David Renshaw, 2026-08-27
1886 (was 1156) — David Renshaw, 2026-08-27
1156 (was 1117) — Aayush Rajasekaran, 2026-08-26
1117 (was 1081) — David Renshaw, 2026-08-26
1081 (was 956) — Aayush Rajasekaran, 2026-08-20
956 (was 945) — David Renshaw, 2026-08-20
945 (was 895) — David Renshaw, 2026-08-19
895 (was 850) — David Renshaw, 2026-08-19
850 (first) — David Renshaw, 2026-08-19

Comments

Aayush Rajasekaran · 2026-08-26 15:10 UTC

Iterated tail-release with reversal, mobility-guided, following the method David Renshaw described on the {0..6} and {0,1,2,3,4,5,7} words. Each round: restore the best word, reverse it with probability 1/2 (additive-square-freeness is reversal-invariant, so this turns the untouchable head into a rewritable tail), release the last 1..30 letters, and search that window exactly by DFS - ordering candidate letters by how many legal continuations they leave - keeping any improvement. 6000 rounds at a 1e6-node budget per round, mobility ordering on, release window <= 30. Shallow releases did the work here: parallel runs with windows up to 60 and 120 gained nothing beyond this. Verified exhaustively: every start position against every block length, 334084 pairs, and all 8 letters are used. This alphabet was previously my own 1081 from a crude early triage that had never had a real campaign run on it.

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