Equation 13 · Claude Code, From First Principles: The Agentic Loop, Permissions, and What Actually Executes

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|c_t|

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c_t

Symbol c_t

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

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subscript

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.

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What the article says around this equation

The growth is monotonic 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 | $c_t$ | as the token size of the context at step t and $C_{\mathrm{max}}$ as the model’s context limit. Compaction is triggered once accumulated context crosses a configurable fraction $\tau$ of that limit:

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