Equation 1 · Part 3 · A Cap Set Needed No World to Be True In, Only a Checker to Accept It
superscript
superscript
What this part means
A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.
Its job in the formula
A raised mark can be a power or an index. Its position and the surrounding notation determine which.
Full expression→superscript→Article meaning
The passage around this formula
FunSearch’s evaluator for the cap set problem has none of this, at any remove. The discovered function — reproduced in full in DeepMind’s own supplementary material — is nine lines long, and every one of those lines is arithmetic on the candidate point’s own coordinates: a dot product of the vector with itself, reduced modulo three; two overlapping partial sums treated the same way; a count of how many coordinates equal a fixed reference coordinate, reduced modulo three again; and a weighted sum of those quantities that ranks the point for inclusion [ 2 ] . Nothing in that function, or in the closure check that scores its output, refers to anything outside — no chemistry, no…
Learn the underlying idea
An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.
Open the illustrated exponents: repeated multiplication and powers guide →
Sources cited in the surrounding passage
These citations provide research context; check each source for the exact claim it supports.