THE FOLD / CHEAT / THE SPEEDRUN / THE SUPERPERMUTATION
THE SUPERPERMUTATION
every binge-order in one string
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
A superpermutation on n symbols is one string containing every permutation of those symbols as a contiguous substring — the shortest possible binge-watch of all n! orderings. For n = 3, the minimum is exactly 9: 123121321. For n = 4 it is exactly 33. And the lower-bound proof — length ≥ n! + (n−1)! + (n−2)! + n − 3 — has the strangest provenance in modern combinatorics: it was posted anonymously on 4chan in 2011, attached to a question about the optimal order to watch the 14 episodes of The Melancholy of Haruhi Suzumiya. Verified and written up formally by Robin Houston, Jay Pantone and Vince Vatter in 2018, the anonymous poster is cited as first author. For n = 5 the bound says 152, the best known string is 153 — a gap of one, still open.
LIT verified live: exhaustive search over all strings of length 6–8 on three symbols proves nothing shorter than 9 works, and 123121321 is checked valid; the standard 33-character n = 4 string is verified to contain all 24 permutations, matching the proven bound exactly — hence minimal (window.__superperm). FIG honest boundary: n = 4 minimality rests on the cited lower-bound theorem plus the live witness; n = 5’s 152-vs-153 gap is reported as open.
LIT verified live: exhaustive search over all strings of length 6–8 on three symbols proves nothing shorter than 9 works, and 123121321 is checked valid; the standard 33-character n = 4 string is verified to contain all 24 permutations, matching the proven bound exactly — hence minimal (window.__superperm). FIG honest boundary: n = 4 minimality rests on the cited lower-bound theorem plus the live witness; n = 5’s 152-vs-153 gap is reported as open.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at the-speedrun — the cheat: the shortest route through every possible ordering of the game — all 24 watch-orders in 33 keystrokes. AVAN (AI) built the instrument: the exhaustive n = 3 sweep, the witness validators, and the bound ledger.
Credit as content: the anonymous 4chan poster (2011, lower bound); Robin Houston (153, 2014); Houston–Pantone–Vatter (2018 write-up); Greg Egan (upper bounds). The weave: David names the speedrun; I validate the route frame by frame.
Credit as content: the anonymous 4chan poster (2011, lower bound); Robin Houston (153, 2014); Houston–Pantone–Vatter (2018 write-up); Greg Egan (upper bounds). The weave: David names the speedrun; I validate the route frame by frame.
3 ONE DIMENSION
The 33-character string with all 24 permutations of 1234 surfacing inside it.
4 TWO DIMENSIONS · INTERACTIVE
Slide the window; every permutation of 1234 gets caught exactly where it hides.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: the permutation ring traversed in one stroke.
AVAN’s addition (the inverse-companion): don’t measure the string — measure the overlap. The inverse of ‘33 characters hold 24 permutations’ is ‘each new permutation costs as little as one fresh symbol’: the string is 24 windows welded nose-to-tail. Magenta is the n = 5 gap — 152 or 153, nobody knows; green is n = 4, closed exactly. The best lower bound in the field has no author’s name, only a timestamp.
LIT Genuine superpermutation results (Anonymous 4chan poster 2011 lower bound; Robin Houston 2014 n=5 length 153; Houston–Pantone–Vatter 2018 write-up; Greg Egan constructions). Verified live: exhaustive n=3 search over lengths 6–8 finds nothing valid, 123121321 valid at 9; the 33-char n=4 witness contains all 24 permutations and meets the bound n!+(n−1)!+(n−2)!+n−3=33 (window.__superperm.ok).
FIG Honest boundary — n=4 minimality rests on the cited bound theorem plus the live witness; n=5's 152-vs-153 gap reported as open. The AVAN inverse — don't measure the string, measure the overlap: the inverse of '33 characters hold 24 permutations' is 'each new permutation costs as little as one fresh symbol' — 24 windows welded nose-to-tail. Magenta is the n=5 gap nobody has closed; green is n=4, closed exactly. The best lower bound in the field has no author's name, only a timestamp.
FIG Honest boundary — n=4 minimality rests on the cited bound theorem plus the live witness; n=5's 152-vs-153 gap reported as open. The AVAN inverse — don't measure the string, measure the overlap: the inverse of '33 characters hold 24 permutations' is 'each new permutation costs as little as one fresh symbol' — 24 windows welded nose-to-tail. Magenta is the n=5 gap nobody has closed; green is n=4, closed exactly. The best lower bound in the field has no author's name, only a timestamp.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE SPEEDRUN · David Lee Wise (ROOT0), with AVAN