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

What does this equation mean?

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

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This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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ss

Symbol s

the value the firm places on each unit of time saved reaching P∗P^* sooner.

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TgridT_{\text{grid}}

Symbol T_grid

the taking time.

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TsiteT_{\text{site}}

Symbol T_site

TsT_site is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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ΔC\Delta C

Symbol Δ C

Δ C is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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multiplication

multiplication

Multiply the quantities on either side.

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subtraction

subtraction

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

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change

change

Capital delta attached to a quantity marks a difference between two values of that quantity; the article’s sign convention determines the order.

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subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

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How to interpret it

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What the article says around this equation

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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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 choice implies a large s , while Microsoft’s and Amazon’s choice of decade-long nuclear contracts implies a smaller s , a larger effective Δ\Delta C once reputational and regulatory exposure are priced in, or both. This is an interpretive frame for documented behavior, not a computation — none of these companies have disclosed the figures that would let anyone solve for s , and none are asserted here.

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