← All parts of this equation

Equation 2 · Part 4 · The Economics, Energy, and Physical Limits of Claude Code and Agentic Development Tools

Symbol c

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

What this part means

the context length.

Its job in the formula

c occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Where the article explains it

where N-active is the number of parameters actively read per token, beta the bytes each occupies at the serving precision, KV of c the memory footprint of the key-value cache at context length c, and BW the accelerator’s memory bandwidth.

The passage around this formula

…analysis of transformer inference efficiency [ 15 ] . Approximately, ttoken  ≳  2 Nactive β+KV(c)BWt_{\mathrm{token}} \;\gtrsim\; \frac{2\,N_{\mathrm{active}}\,\beta + \mathrm{KV}(c)}{\mathrm{BW}}. where N-active is the number of parameters actively read per token, beta the bytes each occupies at the serving precision, KV of c the memory footprint of the key-value cache at context length c, and BW the accelerator’s memory bandwidth. Nothing about pricing changes this floor; it only changes which side of it a given task sits on. Kwon and colleagues showed that KV of c is frequently larger than it needs to be in…

Read this part in the article →

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.

Open the illustrated variables: a letter stands for a value guide →

See this notation across published equations →

Sources cited in the surrounding passage

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