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Equation 12 · How Tool Protocols and the Model Context Protocol Actually Work

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oto_t

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concatenated into the model’s context and fed straight back into πθ\pi_\theta with no protocol-level check on what it contains. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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oto_t

Symbol o_t

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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subscript

subscript

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.

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How to interpret it

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What the article says around this equation

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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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. Whatever a tool returns becomes part of what the model reads next, on exactly the same footing as the user’s own words. Once that is stated plainly, the entire security section below is really just an inventory of what happens when oto_t , or the tool descriptions inside Tt\mathcal{T}_t , are not what they claim to be.

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Sources cited in the article section

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