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Equation 3 · Part 5 · The Frontier Model Landscape in 2035: Four Scenarios, Their Signals, and What Would Falsify Them

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Ctrain(t)≈C0 g t−t0,C_{\text{train}}(t) \approx C_0\, g^{\,t-t_0},
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What this part means

Approximately equal to; the equality is not exact.

Its job in the formula

Approximately equal to; the equality is not exact.

The passage around this formula

Write Ctrain(t)C_{\text{train}}(t) for the cost of the largest training run in year t . Epoch’s estimate is well approximated by simple exponential growth, Ctrain(t)≈C0 g t−t0C_{\text{train}}(t) \approx C_0\, g^{\,t-t_0}. with g between roughly two-point-four and three-point-five depending on method and window [ 5 , 6 ] . The form matters more than the exact rate: exponential cost growth does not by itself predict consolidation. It predicts a shrinking count of organisations able to clear an ever-rising bar only if the pool of adequately capitalised entrants grows more slowly than gtg^{t} . Whether that pool keeps pace is a question about capital markets and state investment, not something the cost curve alone answers — which is exactly why axis…

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A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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