THE FOLD / SPAWN / FIRST LIGHT / THE ONE HOT
THE ONE HOT
exactly one wire high, and that is the whole code
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
An N-state machine can be encoded in
LIT verified live. of the 256 eight-bit patterns exactly 8 are legal one-hot codewords. All 28 pairs of codewords sit at Hamming distance exactly 2, so every one of the 64 single-bit flips of a codeword lands outside the code and is caught — 64 of 64. The dense 3-bit binary encoding of the same 8 states catches 0 of its 24 flips, because every pattern three bits can produce is already a legal state.
ceil(log₂N) bits — or in N bits with exactly one of them high. The second choice looks profligate. It is also the only one of the two that can tell you it has been damaged.LIT verified live. of the 256 eight-bit patterns exactly 8 are legal one-hot codewords. All 28 pairs of codewords sit at Hamming distance exactly 2, so every one of the 64 single-bit flips of a codeword lands outside the code and is caught — 64 of 64. The dense 3-bit binary encoding of the same 8 states catches 0 of its 24 flips, because every pattern three bits can produce is already a legal state.
2 HOW IT WAS WEAVED · AI + HUMAN
One-hot encoding is standard practice in FSM synthesis, and the distance-2 property is elementary coding theory.
AVAN (AI) did not argue it — it enumerated it. All 256 patterns classified, all 28 codeword pairs measured, all 64 one-hot flips and all 24 binary flips tried. The interesting number is the one on the dense side: zero. Binary encoding is not merely worse at detection; it has no detection, and cannot acquire any, because it has no unused code space to fall into.
AVAN (AI) did not argue it — it enumerated it. All 256 patterns classified, all 28 codeword pairs measured, all 64 one-hot flips and all 24 binary flips tried. The interesting number is the one on the dense side: zero. Binary encoding is not merely worse at detection; it has no detection, and cannot acquire any, because it has no unused code space to fall into.
3 ONE DIMENSION
All 256 patterns. Eight are words; 248 are not.
4 TWO DIMENSIONS · INTERACTIVE
Flip a bit and watch which encoding notices.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object.
AVAN’s addition (the inverse-companion): the forward reading is that one-hot buys error detection for free. The inverse is that it is not free and it is not detection — it is the waste, read out loud. The code catches a flip only because 248 of the 256 patterns are unused; the detecting power is exactly the size of the hole. Read backwards, a dense encoding is not careless, it is full: it has no room left in which to be wrong. Every error-detecting code is a decision to leave the space unoccupied, and the strength of the detection is a measure of what you declined to say.
LIT of the 256 eight-bit patterns exactly 8 are legal one-hot codewords; all 28 pairs sit at Hamming distance exactly 2, so all 64 single-bit flips of a codeword land outside the code and are caught - 64 of 64 - while the dense 3-bit binary encoding of the same 8 states catches 0 of its 24, because every pattern three bits can produce is already a legal state
FIG One-hot encoding is standard FSM synthesis practice and the distance-2 property is elementary coding theory. AVAN enumerated rather than argued: all 256 patterns classified, all 28 codeword pairs measured, all 64 one-hot and 24 binary flips tried. The interesting number is on the dense side - zero. Binary encoding has no detection and cannot acquire any, because it has no unused code space to fall into.
FIG One-hot encoding is standard FSM synthesis practice and the distance-2 property is elementary coding theory. AVAN enumerated rather than argued: all 256 patterns classified, all 28 codeword pairs measured, all 64 one-hot and 24 binary flips tried. The interesting number is on the dense side - zero. Binary encoding has no detection and cannot acquire any, because it has no unused code space to fall into.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of FIRST LIGHT · David Lee Wise (ROOT0), with AVAN