Equation 11 · Part 3 · Measuring Tool Protocols and the Model Context Protocol: Evidence, Benchmarks, and Uncertainty

Symbol T_0

n_{\max} \approx (B - T_0)/\bar{t}

T_0

What this part means

the number of tokens.

Its job in the formula

$T_0$ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Full expressionSymbol T_0Article meaning

Where the article explains it

If a system prompt costs $T_0$ tokens before any tools are added, and each of n tools costs on average $\bar{t}$ tokens to describe, total schema overhead is approximately T(n) $\approx$ $T_0$ + n\, $\bar{t}$ .

The passage around this formula

Under a fixed context budget B , the largest catalogue that fits is roughly $n_{\max}$ $\approx$ (B - $T_0$ )/ $\bar{t}$ . The model is a reasonable first approximation, and it is also the assumption a tenfold per-tool variance directly undermines: $\bar t$ is not a constant of the tool, it is a property of how verbosely that tool’s schema and description happen to be written, which is an editorial choice…

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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.

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Sources cited in the surrounding passage

[12] Tool-Schema Compression Enables Agentic RAG Under Constrained Context Budgets ↗

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