Equation 6 · Part 8 · What Actually Happens Inside a Very Long Claude Context Window

Symbol n

C_{\mathrm{LC}} \sim O(n^2 \cdot d), \qquad C_{\mathrm{RAG}} \sim O(k^2 \cdot d), \qquad k \ll n.

n

What this part means

the writing.

Its job in the formula

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

Full expressionSymbol nArticle meaning

Where the article explains it

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: $C_{\mathrm{LC}} \sim O(n^2 \cdot d), \qquad C_{\mathrm{RAG}} \sim O(k^2 \cdot d), \qquad k \ll n$ .

The passage around this formula

…use skips the selection step entirely: the entire candidate 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: $C_{\mathrm{LC}} \sim O(n^2 \cdot d), \qquad C_{\mathrm{RAG}} \sim O(k^2 \cdot d), \qquad k \ll n$ . That gap is not…

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Learn the underlying idea

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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Sources cited in the surrounding passage

[14] Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks ↗

These citations provide research context; check each source for the exact claim it supports.