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Published equation contexts

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

Why this formula appears here

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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PtaskP_{\text{task}}

Symbol P_task

PtP_task 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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q nq^{\,n}

Symbol q^n

qnq^n 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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How to interpret it

Its accuracy depends on the assumptions and range of use described in the article.

Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

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

Equation 5 · Foundation Models

What We Still Cannot Do: Open Problems in Frontier Model Systems

This equation gives an approximation: it relates the quantities while allowing an approximation.

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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