THE FOLD / SPAWN / GENESIS BLOCK / THE NOTHING UP MY SLEEVE
THE NOTHING UP MY SLEEVE
it does not remove the choice, it makes it arguable
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
A cipher needs arbitrary constants. Anyone who chooses them freely could be choosing a backdoor, and nobody could tell. So you do not choose: you take the digits of something that was fixed before you arrived.
LIT verified live — and this one is re-derived here, not quoted. SHA-256’s eight initial hash values are the first 32 bits of the fractional part of the square roots of the first 8 primes. Its sixty-four round constants are the same thing from the cube roots of the first 64 primes. Computed from the primes and compared against the published constants: 8 of 8, 64 of 64 — 72 of 72 exact. sqrt(2) gives 6a09e667; cbrt(2) gives 428a2f98.
LIT verified live — and this one is re-derived here, not quoted. SHA-256’s eight initial hash values are the first 32 bits of the fractional part of the square roots of the first 8 primes. Its sixty-four round constants are the same thing from the cube roots of the first 64 primes. Computed from the primes and compared against the published constants: 8 of 8, 64 of 64 — 72 of 72 exact. sqrt(2) gives 6a09e667; cbrt(2) gives 428a2f98.
2 HOW IT WAS WEAVED · AI + HUMAN
“Nothing-up-my-sleeve” numbers are a convention with real history behind it — DES’s unexplained S-boxes drew suspicion for two decades, and Dual_EC_DRBG’s unexplained points turned out to deserve it.
AVAN (AI) did the only thing that makes this claim mean anything: computed the constants rather than repeating the story. A table of hex values quoted from a standards document and labelled “these come from the primes” is a claim about provenance that nobody checked. Seventy-two independent derivations, all matching, is the check. The constants are not trustworthy because a document says where they came from; they are trustworthy because you can go and get them yourself.
AVAN (AI) did the only thing that makes this claim mean anything: computed the constants rather than repeating the story. A table of hex values quoted from a standards document and labelled “these come from the primes” is a claim about provenance that nobody checked. Seventy-two independent derivations, all matching, is the check. The constants are not trustworthy because a document says where they came from; they are trustworthy because you can go and get them yourself.
3 ONE DIMENSION
Prime, root, fraction, constant. Derived and published, side by side.
4 TWO DIMENSIONS · INTERACTIVE
Walk the constants and check them one at a time.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: constants nobody was free to pick.
AVAN’s addition (the inverse-companion): the forward reading is that deriving constants from the primes proves nobody chose them. The inverse is that somebody chose the primes, the roots, the bit width and the order. Why square roots and not logarithms; why the first eight and not the eighth through fifteenth; why 32 bits from the fraction rather than 40 — each is a free parameter, and a designer with enough of them can still search. Read backwards, nothing-up-my-sleeve does not eliminate the choice; it makes the remaining choices few enough and public enough to be argued about, which is a weaker and far more honest claim.
LIT SHA-256's eight initial hash values are the first 32 bits of the fractional parts of the square roots of the first 8 primes and its sixty-four round constants are the same from the cube roots of the first 64 primes; re-derived here from the primes and compared against the published values, 8 of 8 and 64 of 64 match - 72 of 72 exact, with sqrt(2) giving 6a09e667 and cbrt(2) giving 428a2f98
FIG Nothing-up-my-sleeve numbers are a convention with real history behind them - DES's unexplained S-boxes drew suspicion for two decades and Dual_EC_DRBG's unexplained points turned out to deserve it. AVAN did the only thing that makes the claim mean anything: computed the constants rather than repeating the story. A table of hex quoted from a standard and labelled as coming from the primes is a claim about provenance nobody checked; seventy-two independent derivations, all matching, is the check.
FIG Nothing-up-my-sleeve numbers are a convention with real history behind them - DES's unexplained S-boxes drew suspicion for two decades and Dual_EC_DRBG's unexplained points turned out to deserve it. AVAN did the only thing that makes the claim mean anything: computed the constants rather than repeating the story. A table of hex quoted from a standard and labelled as coming from the primes is a claim about provenance nobody checked; seventy-two independent derivations, all matching, is the check.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of GENESIS BLOCK · David Lee Wise (ROOT0), with AVAN