What does this equation mean?

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 discovered fact, and two indices built from different component sets or different weights are measuring different constructs even when both are called “intelligence.” This is why Artificial Analysis’s own tracked numbers for Grok’s generations — 19 for Grok 3, 34 for Grok 4, and rising to 61 for Grok 4.6 as of its 12 August 2026 write-up [ 8 , 9 ] — should not be expected to match any single headline figure from an xAI launch post, and their disagreement in scale is not evidence that either party is wrong. It is evidence that they are answering different questions. Tellingly, xAI’s own Grok 4.6 marketing leans on this particular outside index directly, describing the model as matching a rival’s score on the Artificial Analysis Intelligence Index specifically [ 9 ] — an instance of a vendor citing an independent evaluator’s own construct because it happens to be favorable, which is a different and more defensible move than issuing an uncontextualized in-house chart, but still a selective citation worth naming as such.