THE FOLD / CHEAT / NOCLIP / THE SIMON
THE SIMON
a hidden mask pinned by linear equations
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Simon’s algorithm finds a hidden bit-mask s that a black box conceals, with an exponential speedup over any classical method. The promise: the function is two-to-one with f(x) = f(x ⊕ s) for a secret s. Classically you must hunt for a colliding pair, needing about 2n/2 queries; Simon’s quantum circuit instead returns, each run, a random vector y with y·s = 0 (mod 2). Gather about n−1 independent such y and a little linear algebra over GF(2) pins s down exactly — a handful of queries where classical needs exponentially many.
LIT verified live: over thousands of hidden masks, collecting n−1 independent measurement vectors and solving the GF(2) system recovers s every time (window.__simon). FIG honest scope: the quantum measurement distribution (uniform over y with y·s = 0) is simulated classically; the linear-algebra recovery is exact.
LIT verified live: over thousands of hidden masks, collecting n−1 independent measurement vectors and solving the GF(2) system recovers s every time (window.__simon). FIG honest scope: the quantum measurement distribution (uniform over y with y·s = 0) is simulated classically; the linear-algebra recovery is exact.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at noclip — the algorithm phases straight through the exponential wall a classical search hits, no-clipping past the collision hunt. AVAN (AI) built the instrument: the measurement sampler (uniform over the orthogonal complement of s) and the GF(2) Gaussian elimination that solves for s.
Credit as content: Daniel Simon (1994), the problem that inspired Shor. The weave: David names the noclip; I confirm n−1 measurements and a GF(2) solve recover the hidden mask exactly.
Credit as content: Daniel Simon (1994), the problem that inspired Shor. The weave: David names the noclip; I confirm n−1 measurements and a GF(2) solve recover the hidden mask exactly.
3 ONE DIMENSION
The oracle is two-to-one: x and x ⊕ s collide. Each measurement returns a y orthogonal to s — a linear constraint on the secret.
4 TWO DIMENSIONS · INTERACTIVE
Collect measurement vectors y (each with y·s = 0); once n−1 are independent, the GF(2) solve returns the hidden s.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: the recovered mask s.
AVAN’s addition (the inverse-companion): don’t hunt for a collision — collect constraints. The inverse of ‘search for x, x⊕s that match’ is ‘each quantum run hands you a y ⊥ s, and n−1 of them determine s by linear algebra.’ Magenta are the orthogonality equations; green is the single mask that satisfies them all. Constraints, not search.
LIT Genuine Simon's algorithm (Daniel Simon, 1994), the problem that inspired Shor: exponential quantum speedup for hidden-XOR-mask. Verified live: over 3000 hidden masks, n−1 independent measurement vectors (each y·s=0) plus GF(2) Gaussian elimination recover s exactly (window.__simon.recoversS).
FIG Honest scope: the quantum measurement distribution (uniform over y with y·s=0) is simulated classically; the linear-algebra recovery is exact. The AVAN inverse is honest — collecting orthogonality constraints y·s=0 and solving over GF(2) (rather than hunting for a colliding pair) is exactly Simon's exponential advantage; magenta are the equations, green the single mask satisfying them all. Constraints, not search.
FIG Honest scope: the quantum measurement distribution (uniform over y with y·s=0) is simulated classically; the linear-algebra recovery is exact. The AVAN inverse is honest — collecting orthogonality constraints y·s=0 and solving over GF(2) (rather than hunting for a colliding pair) is exactly Simon's exponential advantage; magenta are the equations, green the single mask satisfying them all. Constraints, not search.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of NOCLIP · David Lee Wise (ROOT0), with AVAN