Equation 8 · Part 1 · The Economics, Energy, and Physical Limits of Tool Protocols and the Model Context Protocol
Symbol i
What this part means
i is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Its job in the formula
i 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 i→Article meaning
The passage around this formula
Model it simply. Suppose a session runs for k turns, and each turn adds on average tokens of new tool result to a transcript that is resent in full on every request, because nothing is evicting or compressing it. The tokens billed on turn i include roughly i tokens of accumulated result history, so the total billed across the whole session is
Learn the underlying idea
A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.
Open the illustrated variables: a letter stands for a value guide →
See this notation across published equations →
Sources cited in the article section
- [4] Function calling ↗
- [3] Prompt caching ↗
- [7] Lost in the Middle: How Language Models Use Long Contexts ↗
These citations provide research context; check each source for the exact claim it supports.