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Equation 7 · Part 1 · What We Still Cannot Do: Open Problems in Frontier Model Systems

Symbol n_max

nmax⁡≈ln⁡τln⁡q.n_{\max} \approx \frac{\ln \tau}{\ln q}.
nmax⁡n_{\max}

What this part means

the derivative of.

Its job in the formula

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

Where the article explains it

The derivative of nmax⁡n_{\max} with respect to q is steep near q = 1 , which is the good news — small per-step gains buy disproportionate horizon.

The passage around this formula

so the horizon that can be sustained at a target success rate τ\tau is nmax⁡≈ln⁡τln⁡qn_{\max} \approx \frac{\ln \tau}{\ln q}. The derivative of nmax⁡n_{\max} with respect to q is steep near q = 1 , which is the good news — small per-step gains buy disproportionate horizon. The bad news is the same expression read the other way: sustaining an order of magnitude more steps requires driving per-step error down by an order of magnitude, and every…

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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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