Equation 1 · Part 9 · What Independent Evidence Actually Supports About Grok's Capabilities

Starting index or lower bound: i=1

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

i=1

What this part means

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

Its job in the formula

i=1 appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

Full expressionStarting index or lower bound: i=1Article meaning

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

Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.

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Sources cited in the surrounding passage

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