THE FOLD / GRIND / WARM CACHE / THE LZ77 WINDOW
THE LZ77 WINDOW
it finds recent repeats, not repeats
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
LZ77 replaces a repeat with a reference backwards: how far, and how long. It can only reference what is still inside its window, so a pattern that repeats further apart than the window is invisible to it.
LIT verified live. A string with a period of exactly 1,000 characters. At a window of 64 it costs 3,240 tokens and matches 27.8% of the input. At 1,024 — just past the period — it costs 495 and matches 93.8%. Widening to 4,096 changes nothing: 495 again. The window must clear the period, and beyond that it buys nothing.
LIT verified live. A string with a period of exactly 1,000 characters. At a window of 64 it costs 3,240 tokens and matches 27.8% of the input. At 1,024 — just past the period — it costs 495 and matches 93.8%. Widening to 4,096 changes nothing: 495 again. The window must clear the period, and beyond that it buys nothing.
2 HOW IT WAS WEAVED · AI + HUMAN
Lempel and Ziv’s 1977 scheme underlies DEFLATE, zstd and every zip file you have opened.
AVAN (AI) chose a known period so the threshold would be a prediction rather than an observation. The interesting pair is 1,024 and 4,096 giving the identical token count: window size is not a dial that trades memory for ratio smoothly, it is a threshold with a flat region on either side, and the only question is which side of the period you are on.
AVAN (AI) chose a known period so the threshold would be a prediction rather than an observation. The interesting pair is 1,024 and 4,096 giving the identical token count: window size is not a dial that trades memory for ratio smoothly, it is a threshold with a flat region on either side, and the only question is which side of the period you are on.
3 ONE DIMENSION
Window size against tokens. The cliff sits at the period.
4 TWO DIMENSIONS · INTERACTIVE
Move the window across the period.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: a reference reaching backwards.
AVAN’s addition (the inverse-companion): the forward reading is that a bigger window compresses better. The inverse is that the window is a statement about what you expect to matter, made before you look. Everything older is not merely uncompressed — it is unreachable, and the coder cannot tell the difference between data with no redundancy and redundancy it has forgotten. Read backwards, LZ77 does not find repeats; it finds recent repeats, and the ratio you get is a measurement of how well your guess about recency matched the file.
LIT a string with a period of exactly 1,000 characters costs 3,240 tokens at a window of 64 while matching 27.8% of the input, and 495 tokens matching 93.8% at a window of 1,024 - just past the period - with 4,096 giving the identical 495, so the window must clear the period and beyond that buys nothing
FIG Lempel and Ziv's 1977 scheme underlies DEFLATE, zstd and every zip file you have opened. AVAN chose a known period so the threshold would be a prediction rather than an observation. The interesting pair is 1,024 and 4,096 giving the identical token count: window size is not a dial trading memory for ratio smoothly, it is a threshold with a flat region on either side.
FIG Lempel and Ziv's 1977 scheme underlies DEFLATE, zstd and every zip file you have opened. AVAN chose a known period so the threshold would be a prediction rather than an observation. The interesting pair is 1,024 and 4,096 giving the identical token count: window size is not a dial trading memory for ratio smoothly, it is a threshold with a flat region on either side.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of WARM CACHE · David Lee Wise (ROOT0), with AVAN