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Equation 7 · Part 5 · How xAI's Infrastructure Build Compares to the Rest of the Field

multiplication

s⋅(Tgrid−Tsite)>ΔCs \cdot (T_{\text{grid}} - T_{\text{site}}) > \Delta C
multiplication

What this part means

Multiply the quantities on either side.

Its job in the formula

Multiply the quantities on either side.

The passage around this formula

Model the choice as a simple trade. A firm can reach a target power capacity P∗P^* either by waiting for grid interconnection, taking time TgridT_{\text{grid}} , or by generating on site in the shorter time TsiteT_{\text{site}} , at an extra cost Δ\Delta C over grid power — fuel, turbine leasing, and the practical cost of operating ahead of a permit, including the risk of enforcement. Let s be the value the firm places on each unit of time saved reaching P∗P^* sooner. A firm behaves as though it believes s⋅(Tgrid−Tsite)>ΔCs \cdot (T_{\text{grid}} - T_{\text{site}}) > \Delta C. whenever it takes the faster, costlier, more legally exposed route over the slower, cheaper, better-permitted one. The model does not say what s should be; it says xAI’s revealed…

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Learn the underlying idea

Multiplication scales one quantity by another. A dot, a cross, or adjacent symbols can indicate a product.

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