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Equation 6 · Part 2 · RAG in 2035: Four Scenarios, Their Signals, and What Would Falsify Them

Symbol M

cfull(M)=Θ(M),cretrieve(M)=O(log⁡M)+Θ(k),k≪M.c_{\text{full}}(M) = \Theta(M), \qquad c_{\text{retrieve}}(M) = O(\log M) + \Theta(k), \qquad k \ll M.
MM

What this part means

the number of tokens.

Its job in the formula

M is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Where the article explains it

Pasting a whole corpus of size M into context puts a floor under n near M itself; retrieving costs roughly the price of an index lookup plus the price of reasoning over the k ≪\ll M tokens actually returned: cfull(M)=Θ(M),cretrieve(M)=O(log⁡M)+Θ(k),k≪Mc_{\text{full}}(M) = \Theta(M), \qquad c_{\text{retrieve}}(M) = O(\log M) + \Theta(k), \qquad k \ll M.

The passage around this formula

…exactly this partitioning of cost between arithmetic and memory movement in transformer serving [ 5 ] . Write n for the number of tokens a system must hold in an answer’s working set. Pasting a whole corpus of size M into context puts a floor under n near M itself; retrieving costs roughly the price of an index lookup plus the price of reasoning over the k ≪\ll M tokens actually returned: cfull(M)=Θ(M),cretrieve(M)=O(log⁡M)+Θ(k),k≪Mc_{\text{full}}(M) = \Theta(M), \qquad c_{\text{retrieve}}(M) = O(\log M) + \Theta(k), \qquad k \ll M. As a corpus grows, the two costs diverge regardless of how cheap or how large any single model’s…

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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

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