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Equation 9 · Part 1 · Measuring Tool Protocols and the Model Context Protocol: Evidence, Benchmarks, and Uncertainty

Symbol T

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

What this part means

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

Its job in the formula

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

The passage around this formula

…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 function. A recent controlled study of exactly this trade-off tested fourteen models from 1.5B to 32B…

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A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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