Equation 16 · Part 2 · The Economics, Energy, and Physical Limits of Tool Protocols and the Model Context Protocol
subscript
subscript
What this part means
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
Its job in the formula
A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.
Full expression→subscript→Article meaning
The passage around this formula
The assumption doing the work in that formula — every schema injected in full, on every turn, uncompressed — is exactly the assumption Gorilla and ToolLLM abandoned once their tool 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:…
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 →
Sources cited in the surrounding passage
These citations provide research context; check each source for the exact claim it supports.