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Equation 2 · Part 7 · The Economics, Energy, and Physical Limits of Claude Code and Agentic Development Tools

subscript

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

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

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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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the surrounding passage

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