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Equation 1 · Part 2 · A Cap Set Needed No World to Be True In, Only a Checker to Accept It

subscript

Z3n\mathbb{Z}_3^n
subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

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 Z3n\mathbb{Z}_3^n — no chemistry, no…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.