Equation 4 · Part 1 · The Economics, Energy, and Physical Limits of Tool Protocols and the Model Context Protocol

Symbol T_exchange

T_{\mathrm{exchange}}

T_{\mathrm{exchange}}

What this part means

the live user message and the model’s own reply, and the summation term is every prior tool result the session has decided to keep.

Its job in the formula

$T_e$ xchange is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Full expressionSymbol T_exchangeArticle meaning

Where the article explains it

$T_{\mathrm{system}}$ is the operator’s own instructions, $T_{\mathrm{tools}}$ is the serialised cost of every tool schema currently declared, $T_{\mathrm{exchange}}$ is the live user message and the model’s own reply, and the summation term is every prior tool result the session has decided to keep.

The passage around this formula

$T_{\mathrm{system}}$ is the operator’s own instructions, $T_{\mathrm{tools}}$ is the serialised cost of every tool schema currently declared, $T_{\mathrm{exchange}}$ is the live user message and the model’s own reply, and the summation term is every prior tool result the session has decided to keep. The point of writing it this way is that $T_{\mathrm{tools}}$ is paid in full on the very first turn, before a single tool has been called and…

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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 →

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Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.