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Equation 4 · Claude Code, From First Principles: The Agentic Loop, Permissions, and What Actually Executes

What does this equation mean?

ctc_t

Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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ctc_t

Symbol c_t

ctc_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

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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How to interpret it

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What the article says around this equation

Let ctc_t be the context available to the model at step t : system instructions, conversation so far, file contents, tool outputs. The model is a policy π\pi that, given ctc_t , emits either a final answer or a tool call ata_t :

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Sources cited in the article section

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