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Equation 3 · Part 7 · The Frontier Model Landscape in 2035: Four Scenarios, Their Signals, and What Would Falsify Them

subscript

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

What this part means

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.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

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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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

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