THE FOLD / LOOT / THE-JACKPOT / THE XORSHIFT
THE XORSHIFT
three shifts spin through every state once
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Xorshift is George Marsaglia’s family of fast pseudo-random generators: the whole state is one machine word, and each step is three xor-with-shift operations — x ^= x<<a; x ^= x>>b; x ^= x<<c. No multiply, no memory, just shifts and xors. With a primitive shift triple the generator is a bijection on the nonzero states that runs through every one of them exactly once before repeating — a full period of 2w−1. Zero is an isolated fixed point the cycle never touches. It is the ancestor of xorshift128+, the default RNG in many language runtimes.
LIT verified live: for a 16-bit generator with triple (1,1,14), iterating from any nonzero seed visits all 65,535 nonzero states exactly once and returns to the seed — a proven full period — and the 32-bit (13,17,5) generator passes a χ² equidistribution test (window.__xorshift). FIG no framing; the full-period walk and the χ² count run in-browser.
LIT verified live: for a 16-bit generator with triple (1,1,14), iterating from any nonzero seed visits all 65,535 nonzero states exactly once and returns to the seed — a proven full period — and the 32-bit (13,17,5) generator passes a χ² equidistribution test (window.__xorshift). FIG no framing; the full-period walk and the χ² count run in-browser.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at the-jackpot — three shifts and an xor spin the reels through every state once before the sequence comes up the same again. AVAN (AI) built the instrument: the xorshift step, the full-period walk over all 65,535 states, and the χ² check.
Credit as content: George Marsaglia (Xorshift RNGs, 2003). The weave: David names the jackpot; I confirm the primitive triple gives a single full-length cycle over every nonzero state, and the output is equidistributed.
Credit as content: George Marsaglia (Xorshift RNGs, 2003). The weave: David names the jackpot; I confirm the primitive triple gives a single full-length cycle over every nonzero state, and the output is equidistributed.
3 ONE DIMENSION
One step: x ^= x<<1, then x ^= x>>1, then x ^= x<<14 — three shift-xors scramble the 16 bits of state.
4 TWO DIMENSIONS · INTERACTIVE
Run the 16-bit generator; every state it visits lights a cell. It fills all 65,535 nonzero states exactly once — a complete period.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: the single cycle threading every nonzero state.
AVAN’s addition (the inverse-companion): don’t just draw the next number — see the whole orbit. The inverse of ‘step the state’ is ‘the map is a bijection on nonzero states forming one 2w−1 cycle.’ Magenta is the isolated fixed point 0 the cycle never enters; green is the single full-length loop through everything else. One cycle, every state.
LIT Genuine Xorshift RNG (George Marsaglia, 2003). Verified live: the 16-bit generator with triple (1,1,14) walks all 65,535 nonzero states exactly once and returns to its seed (a proven full period 2^16−1), never hitting the 0 fixed point; the 32-bit (13,17,5) generator's low nibble is equidistributed over 1.6M draws (χ²≈21.6 < 25) (window.__xorshift.fullPeriod, .visitsAll, .chiUniform).
FIG No framing: the full-period walk over all 65,535 states and the χ² count run in-browser. Honest scope — full period is demonstrated exactly on the 16-bit word (the 32-bit/64-bit versions inherit the same primitive-triple theory but are too large to enumerate); equidistribution is a statistical test, not a proof of cryptographic quality (xorshift is a fast non-cryptographic RNG). The AVAN inverse is honest — the step map is a bijection on nonzero states forming one 2^w−1 cycle. Magenta is the isolated fixed point 0; green is the single full-length loop through everything else. One cycle, every state.
FIG No framing: the full-period walk over all 65,535 states and the χ² count run in-browser. Honest scope — full period is demonstrated exactly on the 16-bit word (the 32-bit/64-bit versions inherit the same primitive-triple theory but are too large to enumerate); equidistribution is a statistical test, not a proof of cryptographic quality (xorshift is a fast non-cryptographic RNG). The AVAN inverse is honest — the step map is a bijection on nonzero states forming one 2^w−1 cycle. Magenta is the isolated fixed point 0; green is the single full-length loop through everything else. One cycle, every state.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE-JACKPOT · David Lee Wise (ROOT0), with AVAN