THE FOLD / GRIND / BACKPROP / THE ONLY FACTORISATION
THE ONLY FACTORISATION
the drawing IS the number
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
A drawing shows four arms around a centre. Asked whether the picture and the arithmetic agree, the answer turned out stronger than agreement: among equal arm sizes, exactly one reaches the total. 84 = 4096. The four-around-one figure is not a diagram over the number — it is the number’s only four-way equal factorisation.
LIT verified live and then exhaustively. Of the arm sizes 2, 4, 8, 16 and 32, only 8 lands on 4096. Searching every integer arm size from 2 to 4096 returns the same single solution. Four arms of three bits is 12 bits, and 212 is the total.
LIT verified live and then exhaustively. Of the arm sizes 2, 4, 8, 16 and 32, only 8 lands on 4096. Searching every integer arm size from 2 to 4096 returns the same single solution. Four arms of three bits is 12 bits, and 212 is the total.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) logged this under [not asked] and said where it came from: “This was not asked for; it fell out of checking whether the drawing and the arithmetic agreed.” The whole track is two lines of measurement and one conclusion — the only four-way factorisation of the number, not a diagram over it.
AVAN (AI) extended the search from his five sizes to every integer up to the total, because uniqueness among five candidates and uniqueness among all of them are different claims. The stronger one holds: s4 = 4096 has exactly one integer solution, since 4096 = 212 and 12 is divisible by 4 in only one way that yields an integer base.
AVAN (AI) extended the search from his five sizes to every integer up to the total, because uniqueness among five candidates and uniqueness among all of them are different claims. The stronger one holds: s4 = 4096 has exactly one integer solution, since 4096 = 212 and 12 is divisible by 4 in only one way that yields an integer base.
3 ONE DIMENSION
Every equal arm size, and the one that lands.
4 TWO DIMENSIONS · INTERACTIVE
Change the arm count and the arm size.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: four arms of eight around one centre.
AVAN’s addition (the inverse-companion): the forward reading is “the drawing is the number.” The inverse is that uniqueness among EQUAL arms is a much smaller claim than it sounds. Drop the equality and 4096 factors four ways in many shapes — 2×4×16×32, 2×2×32×32, and more. The figure is the only symmetric four-way split, and symmetry was assumed by the drawing before the arithmetic was consulted. Read backwards, the result confirms the picture within an assumption the picture itself supplied.
LIT of the arm sizes 2, 4, 8, 16 and 32 only 8 lands on 4096, and searching every integer arm size from 2 to 4096 returns the same single solution; four arms of three bits is 12 bits, and 2^12 is the total
FIG David logged this under [not asked] and said where it came from: 'This was not asked for; it fell out of checking whether the drawing and the arithmetic agreed.' The whole track is two lines of measurement and one conclusion - the only four-way factorisation of the number, not a diagram over it. AVAN extended the search from his five sizes to every integer up to the total, because uniqueness among five candidates and uniqueness among all of them are different claims. The stronger one holds: s^4 = 4096 has exactly one integer solution, since 4096 = 2^12 and 12 divides by 4 in only one way that yields an integer base.
FIG David logged this under [not asked] and said where it came from: 'This was not asked for; it fell out of checking whether the drawing and the arithmetic agreed.' The whole track is two lines of measurement and one conclusion - the only four-way factorisation of the number, not a diagram over it. AVAN extended the search from his five sizes to every integer up to the total, because uniqueness among five candidates and uniqueness among all of them are different claims. The stronger one holds: s^4 = 4096 has exactly one integer solution, since 4096 = 2^12 and 12 divides by 4 in only one way that yields an integer base.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of BACKPROP · David Lee Wise (ROOT0), with AVAN