THE FOLD / CO-OP / THE SYNC / THE BURROWS-WHEELER
THE BURROWS-WHEELER
a reversible scramble that makes text compress
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
The Burrows–Wheeler transform reversibly reorders a string so that similar characters cluster together — making it far more compressible — yet the original can be perfectly reconstructed from the transform plus one index. It takes the last column of the sorted table of all rotations of the string. Astonishingly, that last column, though scrambled, holds enough to invert the whole thing. It is the heart of bzip2 and of FM-index text search.
LIT verified live: over 200 random strings, inverting the BWT (last column + index) returns the exact original (window.__bwt). FIG no framing; exact and lossless.
LIT verified live: over 200 random strings, inverting the BWT (last column + index) returns the exact original (window.__bwt). FIG no framing; exact and lossless.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at the-sync — a reversible reordering both sides can undo to recover the exact data. The BWT is that lossless scramble. AVAN (AI) built the instrument: the rotation table, the sort, the last-column extraction, the repeated-sort inversion, and the round-trip check.
Credit as content: Michael Burrows & David Wheeler (1994). The weave: David names the-sync; I sort all rotations, take the last column, and rebuild the original by repeatedly prepending and sorting — confirming the scramble is perfectly reversible.
Credit as content: Michael Burrows & David Wheeler (1994). The weave: David names the-sync; I sort all rotations, take the last column, and rebuild the original by repeatedly prepending and sorting — confirming the scramble is perfectly reversible.
3 ONE DIMENSION
“banana” → sort all 6 rotations → read the last column: nnbaaa. The a’s and n’s have clustered — more compressible — yet an index lets you invert it exactly.
4 TWO DIMENSIONS · INTERACTIVE
A string, its rotation table sorted, the BWT last column, and the reconstruction — checked to return the original.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: a reordering that clusters, yet fully inverts.
AVAN’s addition (the inverse-companion): make a string more compressible without losing anything — sort its rotations and take the last column, which clusters like characters, and keep one index so the whole thing inverts. The inverse of ‘compress by finding patterns in place’ is ‘permute so patterns line up — reversibly.’ Magenta is the scattered original; green is the clustered, invertible transform. A lossless scramble that helps you pack.
LIT Genuine Burrows-Wheeler transform (Burrows & Wheeler 1994). Verified live: over 200 random strings, taking the last column of the sorted rotation table (plus the original-row index) and inverting it by repeated prepend-and-sort returns the exact original string (window.__bwt.reversible); 'banana' -> 'nnbaaa'.
FIG No framing: the rotation table, the sort, the last-column extraction, the repeated-sort inversion, and the round-trip check run in-browser and hold losslessly. The AVAN inverse is honest — sorting rotations and taking the last column clusters like characters (more compressible) while one index keeps it invertible; magenta is the scattered original, green the clustered invertible transform. A lossless scramble that helps you pack.
FIG No framing: the rotation table, the sort, the last-column extraction, the repeated-sort inversion, and the round-trip check run in-browser and hold losslessly. The AVAN inverse is honest — sorting rotations and taking the last column clusters like characters (more compressible) while one index keeps it invertible; magenta is the scattered original, green the clustered invertible transform. A lossless scramble that helps you pack.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE SYNC · David Lee Wise (ROOT0), with AVAN