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Equation 17 · Part 3 · Claude Code, From First Principles: The Agentic Loop, Permissions, and What Actually Executes

Symbol C_max

∣ct∣>τ⋅Cmax  ⟹  ct→c^t,∣c^t∣≪∣ct∣.|c_t| > \tau \cdot C_{\mathrm{max}} \implies c_t \to \hat{c}_t, \quad |\hat{c}_t| \ll |c_t|.
CmaxC_{\mathrm{max}}

What this part means

CmC_max 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

CmC_max is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

…and the response is a threshold rule, which is worth writing down because it is the one piece of real mechanism in this section rather than product description. Treat |ctc_t| as the token size of the context at step t and CmaxC_{\mathrm{max}} as the model’s context limit. Compaction is triggered once accumulated context crosses a configurable fraction τ\tau of that limit: ∣ct∣>τ⋅Cmax  ⟹  ct→c^t,∣c^t∣≪∣ct∣|c_t| > \tau \cdot C_{\mathrm{max}} \implies c_t \to \hat{c}_t, \quad |\hat{c}_t| \ll |c_t|. Concretely, Claude Code “clears older tool outputs first, then summarizes the conversation if needed,” preserving “requests and…

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A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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