Equation 1 · Part 7 · The Economics, Energy, and Physical Limits of Tool Protocols and the Model Context Protocol
Symbol T_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
xchange is one of the signed contributions combined to compute the quantity on the left.
Full expression→Symbol T_exchange→Article meaning
Where the article explains it
is the operator’s own instructions, is the serialised cost of every tool schema currently declared, 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
…to write out what actually occupies a turn’s context budget: . is the operator’s own instructions, is the serialised cost of every tool schema currently declared, 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 is paid in full on the very first turn, before a single tool has been called and…
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
- [1] Model Context Protocol Specification (2025-06-18) ↗
- [4] Function calling ↗
- [5] Gorilla: Large Language Model Connected with Massive APIs ↗
- [6] ToolLLM: Facilitating Large Language Models to Master 16000+ Real-world APIs ↗
- [12] MCP Security Notification: Tool Poisoning Attacks ↗
These citations provide research context; check each source for the exact claim it supports.