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Equation 6 · Part 7 · What Actually Happens Inside a Very Long Claude Context Window

Symbol k

CLC∼O(n2⋅d),CRAG∼O(k2⋅d),k≪n.C_{\mathrm{LC}} \sim O(n^2 \cdot d), \qquad C_{\mathrm{RAG}} \sim O(k^2 \cdot d), \qquad k \ll n.
kk

What this part means

k 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

k 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

…material goes into the window, and the burden of finding what matters is placed on attention at inference time rather than on an index built in advance. Writing n for the number of tokens placed directly in context and k for the number of tokens a retriever would instead have selected, the quadratic cost derived above means the two approaches sit in different complexity regimes for handling the same underlying material: CLC∼O(n2⋅d),CRAG∼O(k2⋅d),k≪nC_{\mathrm{LC}} \sim O(n^2 \cdot d), \qquad C_{\mathrm{RAG}} \sim O(k^2 \cdot d), \qquad k \ll n. That gap is not an incidental efficiency detail. It is the reason…

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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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