← All parts of this equation

Equation 9 · Part 7 · Measuring Tool Protocols and the Model Context Protocol: Evidence, Benchmarks, and Uncertainty

subscript

T(n)≈T0+n tˉ.T(n) \approx T_0 + n\,\bar{t}.
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

A simple linear model makes the assumption underneath that spread explicit. If a system prompt costs T0T_0 tokens before any tools are added, and each of n tools costs on average tˉ\bar{t} tokens to describe, total schema overhead is approximately T(n)≈T0+n tˉT(n) \approx T_0 + n\,\bar{t}. Under a fixed context budget B , the largest catalogue that fits is roughly nmax⁡n_{\max} ≈\approx (B - T0T_0)/tˉ\bar{t} . The model is a reasonable first approximation, and it is also the assumption a tenfold per-tool variance directly undermines: tˉ\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 rather than a physical fact about the…

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 →

Sources cited in the surrounding passage

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