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Equation 15 · Part 2 · How Tool Protocols and the Model Context Protocol Actually Work

subscript

Tt\mathcal{T}_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

Here Tt\mathcal{T}_t is the tool set most recently returned by tools/list , each member carrying its own schema; πθ\pi_\theta is the model, which is expected — but not forced by anything outside its own training — to emit a call ata_t whose name and arguments validate against some tool in Tt\mathcal{T}_t ; Call\mathrm{Call} is dispatch through the client to the server and back, exactly as described above; and ht+1h_{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: oto_t is concatenated into the model’s context and fed straight back into πθ\pi_\theta with no protocol-level check on what it contains.…

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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.

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the article section

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