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Equation 7 · Part 1 · What Actually Happens Inside a Very Long Claude Context Window

Symbol O

O(k2)O(k^2)
OO

What this part means

O 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

O 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

Two. Hybrid retrieval-plus-long-context architectures, in the Self-Route style, become the default production pattern for large, heterogeneous document collections, with a full long-context pass reserved for queries a cheaper first pass flags as difficult, on the assumption that the cost asymmetry between O(k2k^2) and O(n2n^2) processing does not disappear as windows grow further. Disconfirmed if , by 2028, production systems handling large heterogeneous corpora have converged on feeding full context on every request as the standard approach, with no routing step.

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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