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Equation 11 · Part 1 · Measuring Tool Protocols and the Model Context Protocol: Evidence, Benchmarks, and Uncertainty

Symbol n_max

nmax⁡≈(B−T0)/tˉn_{\max} \approx (B - T_0)/\bar{t}
nmax⁡n_{\max}

What this part means

nmn_max 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

nmn_max 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

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…

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