Numerator: 100,000

The passage around this formula

xAI announced a doubling of the original cluster to 200,000 GPUs within roughly ninety days of the initial buildout, adding Nvidia H200s alongside the original H100s [ 16 ] . That kind of headline — “doubled in ninety-two days” — is easy to read two different ways, and the difference matters for judging how the next expansion phase should be interpreted. Read as a constant installation rate, doubling 100,000 GPUs to 200,000 over ninety-two days implies roughly $r = \frac{100{,}000}{92} \approx 1{,}087 \text{ GPUs installed per day.}$. Read instead as a constant compounding rate — the assumption implicit whenever a “doubled again” claim is extrapolated forward — the same ninety-two-day doubling implies a daily multiplicative growth rate g solving…

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