Equation 16 · Part 1 · The Economics, Energy, and Physical Limits of Tool Protocols and the Model Context Protocol
Symbol bart_tool
What this part means
the number of tokens.
Its job in the formula
barool is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Full expression→Symbol bart_tool→Article meaning
Where the article explains it
If every tool schema costs on average tokens and all of them are injected in full on every turn, the maximum number of tools a deployment can nominally offer before it must start pruning or retrieving is = .
The passage around this formula
…catalogues grew past a few dozen entries, replacing blanket injection with retrieval that surfaces a handful of relevant tool descriptions per request instead of the whole catalogue [ 5 , 6 ] . That substitution changes from “every tool’s cost, always” to “a few tools’ cost, most of the time,” which is the only lever in the equation that scales sublinearly as the number of available tools grows. It is also, notably, a departure from what MCP’s own discovery model assumes by default:…
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A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.
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Sources cited in the surrounding passage
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