Equation 6 · Part 1 · Claude Code, From First Principles: The Agentic Loop, Permissions, and What Actually Executes

Symbol a_t

a_t = \pi(c_t).

a_t

What this part means

$a_t$ is part of the quantity the equation computes from the expression on the right.

Its job in the formula

$a_t$ is part of the quantity the equation computes from the expression on the right.

Full expressionSymbol a_tArticle meaning

The passage around this formula

Let $c_t$ be the context available to the model at step t : system instructions, conversation so far, file contents, tool outputs. The model is a policy $\pi$ that, given $c_t$ , emits either a final answer or a tool call $a_t$ : $a_t = \pi(c_t)$ . Claude Code executes $a_t$ — subject to a permission check described in the next section — against the real filesystem, shell, or network, producing an observation $o_t$ : a diff applied, a command’s stdout and exit code, a search result. That observation is appended to the context for the next step:

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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.

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Sources cited in the article section

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