← All parts of this equation

Equation 1 · Part 6 · What Independent Evidence Actually Supports About Grok's Capabilities

=

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

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

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=∑i=1nwi si,∑i=1nwi=1I = \sum_{i=1}^{n} w_i \, s_i, \qquad \sum_{i=1}^{n} w_i = 1. where each sis_i is a model’s normalized score on component benchmark i and each wiw_i is a weight chosen by whoever maintains the index. That weight vector is an editorial decision, not a…

Read this part in the article →

Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

Open the illustrated equality: what the equals sign claims guide →

Sources cited in the surrounding passage

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