What does this equation mean?

A useful way to see the shape of the tax is to write out what actually occupies a turn’s context budget: $T_{\mathrm{turn}} = T_{\mathrm{system}} + T_{\mathrm{tools}} + \sum_{i=1}^{n} T_{\mathrm{result},i} + T_{\mathrm{exchange}}$. $T_{\mathrm{system}}$ 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 before it is known whether any tool will be needed at all. A deployment that registers thirty MCP servers, each exposing a handful of tools with a paragraph of description and a nested JSON Schema, can easily spend several thousand tokens of every request on a catalogue the model consults for perhaps one or two entries. That is not a defect in any particular implementation; it is a direct consequence of a protocol whose entire purpose is to describe capability generically, to a reader who cannot be assumed to already know it.