Equation 1 · Part 8 · What Independent Evidence Actually Supports About Grok's Capabilities

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I = \sum_{i=1}^{n} w_i \, s_i, \qquad \sum_{i=1}^{n} w_i = 1,

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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.

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The passage around this formula

This is also where a composite measure earns its own paragraph, because a composite index is not a repeat measurement of a single-benchmark headline claim — it is a different object. Artificial Analysis, an independent evaluation firm that runs every model it tracks through one fixed harness, reports an “Intelligence Index” built from nine separate evaluations, including Humanity’s Last Exam and GPQA Diamond among others [ 8 ] . A composite index of this kind is, formally, a weighted sum $I = \sum_{i=1}^{n} w_i \, s_i, \qquad \sum_{i=1}^{n} w_i = 1$ . where each $s_i$ is a model’s normalized score on component benchmark i and each $w_i$ is a weight chosen by whoever maintains the index. That weight vector is an editorial decision, not a…

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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.

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Sources cited in the surrounding passage

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