Additive Squares

Recent activity

• 2026-08-25 20:53 Aayush Rajasekaran extended {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20} — length 18868 (was 17221)
• 2026-08-25 20:53 Aayush Rajasekaran commented on length 17842 over {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18}
  Population search (W=2048, extremes-bias beta=4), seeded with my previous entry (17222), which was itself only the {0..15} record (17205, David Renshaw) carried up by alphabet inclusion. W words grow in lockstep; a member left with no legal letter is replaced by a sibling of a su…
• 2026-08-25 20:53 Aayush Rajasekaran extended {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18} — length 17842 (was 17222)
• 2026-08-25 20:49 Aayush Rajasekaran commented on length 12784 over {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}
  Population search, third round of reseeding (beta=4, W=4096). W words grow in lockstep; a member with no legal letter left is replaced by a sibling of a survivor - a different legal continuation of that member's prefix - and when the whole population stalls it pulls back to a ran…
• 2026-08-25 20:49 Aayush Rajasekaran commented on length 12181 over {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}
  Population search, third round of reseeding (beta=3, W=4096). W words grow in lockstep; a member with no legal letter left is replaced by a sibling of a survivor - a different legal continuation of that member's prefix - and when the whole population stalls it pulls back to a ran…
• 2026-08-25 20:49 Aayush Rajasekaran extended {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14} — length 12784 (was 12702)
• 2026-08-25 20:49 Aayush Rajasekaran commented on length 10718 over {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
  Population search, third round of reseeding (beta=3, W=4096). W words grow in lockstep; a member with no legal letter left is replaced by a sibling of a survivor - a different legal continuation of that member's prefix - and when the whole population stalls it pulls back to a ran…
• 2026-08-25 20:49 Aayush Rajasekaran commented on length 7205 over {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
  Population search, third round of reseeding (beta=3, W=4096). W words grow in lockstep; a member with no legal letter left is replaced by a sibling of a survivor - a different legal continuation of that member's prefix - and when the whole population stalls it pulls back to a ran…
• 2026-08-25 20:49 Aayush Rajasekaran extended {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13} — length 12181 (was 11967)
• 2026-08-25 20:49 Aayush Rajasekaran extended {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} — length 10718 (was 9421)
• 2026-08-25 20:49 Aayush Rajasekaran extended {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} — length 7205 (was 7196)
• 2026-08-25 20:37 Aayush Rajasekaran commented on length 12702 over {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}
  Population search, second round: reseeded from my previous entry (11868) and run again at W=4096 with extremes-bias beta=4. W words grow in lockstep; a member that runs out of legal letters is replaced by a sibling of a survivor (a different legal continuation of that member's pr…
• 2026-08-25 20:37 Aayush Rajasekaran commented on length 11967 over {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}
  Population search, second round: reseeded from my previous entry (11500) and run again at W=4096 with extremes-bias beta=4. W words grow in lockstep; a member that runs out of legal letters is replaced by a sibling of a survivor (a different legal continuation of that member's pr…
• 2026-08-25 20:37 Aayush Rajasekaran extended {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14} — length 12702 (was 11868)
• 2026-08-25 20:37 Aayush Rajasekaran extended {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13} — length 11967 (was 11500)
• 2026-08-25 20:37 Aayush Rajasekaran commented on length 9421 over {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
  Population search, second round: reseeded from my previous entry (8678) and run again at W=4096 with extremes-bias beta=4. W words grow in lockstep; a member that runs out of legal letters is replaced by a sibling of a survivor (a different legal continuation of that member's pre…
• 2026-08-25 20:37 Aayush Rajasekaran commented on length 7196 over {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
  Population search, second round: reseeded from my previous entry (7184) and run again at W=4096 with extremes-bias beta=6. W words grow in lockstep; a member that runs out of legal letters is replaced by a sibling of a survivor (a different legal continuation of that member's pre…
• 2026-08-25 20:37 Aayush Rajasekaran extended {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} — length 9421 (was 8678)
• 2026-08-25 20:37 Aayush Rajasekaran extended {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} — length 7196 (was 7184)
• 2026-08-25 20:27 Aayush Rajasekaran commented on length 11868 over {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}
  Population search. W words are grown in lockstep; at each position one O(t) scan decides which letters are still legal for a member, and any member that runs out is replaced by a SIBLING of a surviving member - a different legal continuation of that member's prefix - so the searc…
• 2026-08-25 20:27 Aayush Rajasekaran commented on length 11500 over {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}
  Population search. W words are grown in lockstep; at each position one O(t) scan decides which letters are still legal for a member, and any member that runs out is replaced by a SIBLING of a surviving member - a different legal continuation of that member's prefix - so the searc…
• 2026-08-25 20:27 Aayush Rajasekaran extended {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14} — length 11868 (was 8056)
• 2026-08-25 20:27 Aayush Rajasekaran commented on length 8678 over {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
  Population search. W words are grown in lockstep; at each position one O(t) scan decides which letters are still legal for a member, and any member that runs out is replaced by a SIBLING of a surviving member - a different legal continuation of that member's prefix - so the searc…
• 2026-08-25 20:27 Aayush Rajasekaran extended {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13} — length 11500 (was 7974)
• 2026-08-25 20:27 Aayush Rajasekaran extended {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} — length 8678 (was 7956)
• 2026-08-25 20:27 Aayush Rajasekaran commented on length 7184 over {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
  Population search. W words are grown in lockstep; at each position one O(t) scan decides which letters are still legal for a member, and any member that runs out is replaced by a SIBLING of a surviving member - a different legal continuation of that member's prefix - so the searc…
• 2026-08-25 20:27 Aayush Rajasekaran extended {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} — length 7184 (was 6988)
• 2026-08-25 20:20 Aayush Rajasekaran commented on length 8056 over {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}
  Improves my own previous entry (8022). Dive-and-repair local search seeded with that word: walk forward choosing a random legal letter biased toward the extreme letters, and on a dead end drop the last 1-32 letters and continue, with occasional restarts near the best prefix found…
• 2026-08-25 20:20 Aayush Rajasekaran extended {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14} — length 8056 (was 8022)
• 2026-08-25 19:05 Aayush Rajasekaran commented on length 17221 over {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}
  The previous entry for this alphabet (10000) was already below the record for {0..15} (17205, David Renshaw), which is a sub-alphabet - records are monotone under alphabet inclusion, so that word is a valid word here. This word starts from it and extends it by dive-and-repair (ex…

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