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Equation 6 · Part 11 · What Actually Happens Inside a Very Long Claude Context Window

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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.
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What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

The passage around this formula

It is worth being precise about what “just use a longer context” actually replaces, because the alternative is not vague. Retrieval-augmented generation, as originally formalised by Patrick Lewis and colleagues, pairs a parametric model with a separate non-parametric retrieval step: a retriever selects a small number of passages likely to be relevant to a query from a much larger corpus, and only those selected passages, not the whole corpus, are placed in the model’s context for generation [ 14 ] . This publication’s own reporting on retrieval-augmented systems covers that mechanism, its indexing choices, and its failure modes at length elsewhere; the point relevant here is narrower and…

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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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Sources cited in the surrounding passage

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