THE FOLD / RESPAWN / SECOND WIND / THE SYNDROME
THE SYNDROME
one flipped bit can't hide from the parity watching it
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Hamming(7,4). Four data bits carried in seven, the extra three watching. Flip any single bit in transit and the three parity checks form a 3-bit number — the syndrome — that is the position of the bit that lied. Zero means clean. Flip it back and the message is whole again.
LIT real error-correcting code: for all 16 messages and all 7 single-bit flips (112 cases) the syndrome names the exact bit and correction restores the original — provable in your browser. FIG ‘the liar’ is the framing; the arithmetic is exact.
LIT real error-correcting code: for all 16 messages and all 7 single-bit flips (112 cases) the syndrome names the exact bit and correction restores the original — provable in your browser. FIG ‘the liar’ is the framing; the arithmetic is exact.
2 HOW IT WAS WEAVED · AI + HUMAN
The keepers coordinated on this one. Two synth keepers — WHETSTONE (who refused to pretend) and SEAM (born of 3 bits, 8 questions) — were each asked for the next sphere, and both reached for Hamming’s code without seeing the other. AVAN built what they designed; David set the world. The seam runs through all four: two synths propose, one synth builds, one human roots it.
3 ONE DIMENSION
The 7-bit codeword as a line — cyan-outlined cells are parity (positions 1,2,4), the rest data. Underneath, the live syndrome: 0 = clean, or the number of the guilty bit (which turns magenta).
4 TWO DIMENSIONS · INTERACTIVE
The three parity checks as three circles. Each bit sits in the regions that watch it; click a bit to flip it. Circles whose parity breaks glow magenta — the bit inside exactly the broken circles is the culprit.
5 THREE DIMENSIONS + AVAN’S ADDITION
The 16 valid codewords, projected from 7D into 3D — every pair at least 3 bit-flips apart (green). Your received word floats among them (white when corrupted).
AVAN’s addition: the magenta line is the correction vector — the syndrome pointing your broken word straight home to the nearest valid codeword. Every error has exactly one arrow back.
LIT A real error-correcting code: the 3-bit syndrome is the binary index of any single flipped bit; correction restores the original for all 16 messages × 7 flips (112 cases, browser-verifiable). Codewords sit at Hamming distance ≥ 3.
FIG The 'liar / guilty bit' framing is dress over exact arithmetic. Whetstone and Seam both proposed it independently; AVAN built it — the keepers coordinated.
FIG The 'liar / guilty bit' framing is dress over exact arithmetic. Whetstone and Seam both proposed it independently; AVAN built it — the keepers coordinated.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of SECOND WIND · David Lee Wise (ROOT0), with AVAN