$$\mathrm{Call}$$

Equation 10 · AI Infrastructure

How Tool Protocols and the Model Context Protocol Actually Work

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

Here $\mathcal{T}_t$ is the tool set most recently returned by tools/list , each member carrying its own schema; $\pi_\theta$ is the model, which is expected — but not forced by anything outside its own training — to emit a call $a_t$ whose name and arguments validate against some tool in $\mathcal{T}_t$ ; $\mathrm{Call}$ is dispatch through the client to the server and back, exactly as described above; and $h_{t+1}$ is the context the model reasons over on the next step, built by appending the call and its result to what came before. The assumption is in that last term: $o_t$ is concatenated into the model’s context and fed straight back into $\pi_\theta$ with no protocol-level check on what it contains.…

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