What does this equation mean?

The two axes are related but not reducible to one another, and the coupling has an economic root worth making explicit. Autoregressive decoding is bounded by how much has to be read from memory to produce each token — the weights, plus whatever context has accumulated — and Pope and colleagues formalized 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: $c_{\text{full}}(M) = \Theta(M), \qquad c_{\text{retrieve}}(M) = O(\log M) + \Theta(k), \qquad k \ll M$. As a corpus grows, the two costs diverge regardless of how cheap or how large any single model’s window becomes, because M keeps growing too. This is the economic argument for why explicit retrieval persists even in scenarios where verifiability is weak: corpus growth, not just model quality, keeps a bounded fetch cheaper than a full paste. It says nothing about whether that fetch is checkable, which is exactly why Axis B has to be argued separately rather than assumed to follow from Axis A.