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Equation 1 · Part 4 · Why Claude Code Delegates to Subagents, and What That Actually Buys You

Symbol k

Ttotal=Tparent+∑i=1kTsubagenti,Tparent≪∑i=1kTsubagenti.T_{\mathrm{total}} = T_{\mathrm{parent}} + \sum_{i=1}^{k} T_{\mathrm{subagent}_i}, \qquad T_{\mathrm{parent}} \ll \sum_{i=1}^{k} T_{\mathrm{subagent}_i}.
kk

What this part means

k appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

Its job in the formula

k appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

The passage around this formula

…it relocates where that computation’s output lands: Ttotal=Tparent+∑i=1kTsubagenti,Tparent≪∑i=1kTsubagentiT_{\mathrm{total}} = T_{\mathrm{parent}} + \sum_{i=1}^{k} T_{\mathrm{subagent}_i}, \qquad T_{\mathrm{parent}} \ll \sum_{i=1}^{k} T_{\mathrm{subagent}_i}. The parent conversation’s occupied share of its own window, TparentT_{\mathrm{parent}} , stays small and bounded even as the total work performed across k delegated subagents grows without bound. That inequality is the real content behind the phrase “context savings” — the saving is measured in the one window that has to keep attending to everything else in the task, not in total tokens billed.

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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.

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Sources cited in the surrounding passage

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