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Equation 5 · Part 2 · What We Still Cannot Do: Open Problems in Frontier Model Systems

Symbol q^n

Ptask≈q n,P_{\text{task}} \approx q^{\,n},
q nq^{\,n}

What this part means

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

Its job in the formula

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

The passage around this formula

There is a second, compounding reason, and it is quantitative. Consider a task decomposed into n dependent steps, each completed correctly with probability q , where an uncaught error propagates. Success over the whole task goes as Ptask≈q nP_{\text{task}} \approx q^{\,n}. so the horizon that can be sustained at a target success rate τ\tau is

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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