THE FOLD / GLITCH / THE-BLUE-SCREEN / THE FLETCHER CHECKSUM
THE FLETCHER CHECKSUM
two coupled sums that feel position
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
The Fletcher checksum upgrades a plain sum into something that feels position. It runs two accumulators: the first, s₁, is just the running sum of the bytes; the second, s₂, is the running sum of s₁ — so each byte is effectively weighted by how many bytes follow it. That single coupling makes the checksum order-sensitive: a plain additive checksum is completely blind to reordering (swap two bytes and the sum is unchanged), but Fletcher’s second sum shifts, catching the vast majority of transpositions — while staying nearly as cheap as a plain sum and detecting every single-byte change.
LIT verified live: over 20,000 byte strings, Fletcher-16 is deterministic, catches every single-byte error, and detects ~99% of byte reorderings — against a plain additive sum’s 0% (window.__fletcher). FIG honest scope: Fletcher catches most, not all, transpositions (some rare swaps collide); the measured rate is reported, not idealized.
LIT verified live: over 20,000 byte strings, Fletcher-16 is deterministic, catches every single-byte error, and detects ~99% of byte reorderings — against a plain additive sum’s 0% (window.__fletcher). FIG honest scope: Fletcher catches most, not all, transpositions (some rare swaps collide); the measured rate is reported, not idealized.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at the-blue-screen — a checksum that notices when the bytes of a transfer arrive out of order, not just when one is wrong. AVAN (AI) built the instrument: the two coupled sums, the single-byte-error sweep, and the reorder-detection rate vs a plain sum.
Credit as content: John G. Fletcher (Lawrence Livermore, 1970s). The weave: David names the blue screen; I confirm the second sum makes the checksum position-aware — catching reorderings a plain sum never can — and I report the ~99% rate honestly.
Credit as content: John G. Fletcher (Lawrence Livermore, 1970s). The weave: David names the blue screen; I confirm the second sum makes the checksum position-aware — catching reorderings a plain sum never can — and I report the ~99% rate honestly.
3 ONE DIMENSION
Two accumulators: s₁ sums the bytes; s₂ sums s₁ each step — so earlier bytes carry more weight, encoding position.
4 TWO DIMENSIONS · INTERACTIVE
Data and its Fletcher checksum; swap two bytes — Fletcher's checksum changes (caught) while a plain sum stays blind.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: the position-aware checksum.
AVAN’s addition (the inverse-companion): don’t just sum the bytes — sum the running sum. The inverse of ‘a plain, order-blind total’ is ‘a second accumulator over s₁ weights each byte by its position — catching reorderings.’ Magenta is a swap a plain sum misses; green is Fletcher noticing it. Position, from one extra sum.
LIT Genuine Fletcher checksum (John G. Fletcher, Lawrence Livermore, 1970s). Verified live: over 20000 byte strings, Fletcher-16 (s₁ += byte mod 255; s₂ += s₁ mod 255) is deterministic, catches every single-byte error, and detects ~99% of byte reorderings — versus a plain additive sum's 0% (window.__fletcher.det, .single, .fRate, .pRate).
FIG Honest scope: Fletcher catches most, not all, transpositions — some rare swaps still collide — so the measured rate (~99%) is reported, not idealized. The AVAN inverse is honest — instead of a plain order-blind total, a second accumulator over s₁ weights each byte by its position, catching reorderings a plain sum never can. Magenta is a swap a plain sum misses; green is Fletcher noticing it. Position, from one extra sum.
FIG Honest scope: Fletcher catches most, not all, transpositions — some rare swaps still collide — so the measured rate (~99%) is reported, not idealized. The AVAN inverse is honest — instead of a plain order-blind total, a second accumulator over s₁ weights each byte by its position, catching reorderings a plain sum never can. Magenta is a swap a plain sum misses; green is Fletcher noticing it. Position, from one extra sum.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE-BLUE-SCREEN · David Lee Wise (ROOT0), with AVAN