← All parts of this equation

Equation 15 · Part 3 · The Economics, Energy, and Physical Limits of Tool Protocols and the Model Context Protocol

Symbol T_system

nmax⁡=⌊C−Tsystem−Treservetˉtool⌋.n_{\max} = \left\lfloor \frac{C - T_{\mathrm{system}} - T_{\mathrm{reserve}}}{\bar{t}_{\mathrm{tool}}} \right\rfloor.
TsystemT_{\mathrm{system}}

What this part means

the fixed cost of operator instructions.

Its job in the formula

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

Where the article explains it

Let C be the model’s usable context window, TsystemT_{\mathrm{system}} the fixed cost of operator instructions, and TreserveT_{\mathrm{reserve}} a reserved allowance for the user’s message and the model’s own answer.

The passage around this formula

…comes into focus: given a fixed context window, how many tools can actually be offered before something has to give? A simple ceiling model makes the trade-off explicit. Let C be the model’s usable context window, TsystemT_{\mathrm{system}} the fixed cost of operator instructions, and TreserveT_{\mathrm{reserve}} a reserved allowance for the user’s message and the model’s own answer. If every tool schema costs on average tˉtool\bar{t}_{\mathrm{tool}} tokens and all of them are injected in full on every turn, the maximum number…

Read this part in the article →

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 →

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.