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Equation 2 · Part 1 · The Economics, Energy, and Physical Limits of Claude Code and Agentic Development Tools

Symbol t_token

ttoken  ≳  2 Nactive β+KV(c)BW,t_{\mathrm{token}} \;\gtrsim\; \frac{2\,N_{\mathrm{active}}\,\beta + \mathrm{KV}(c)}{\mathrm{BW}},
ttokent_{\mathrm{token}}

What this part means

ttt_token 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

ttt_token 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

Underneath all of the pricing mechanics sits a constraint pricing cannot remove: generating one token from a large language model is, for most of a request, bound by how fast bytes can move through accelerator memory rather than by how much arithmetic the accelerator can perform. Producing each token requires reading the model’s active weights and the accumulated key-value cache for that request from memory once; the arithmetic performed per byte read is low, so decoding is memory-bandwidth-bound while only the initial processing of a long prompt is compute-bound, a distinction Pope and colleagues formalized in their analysis of transformer inference efficiency [ 15 ] . Approximately,…

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