Equation 6 · Part 2 · Claude Code, From First Principles: The Agentic Loop, Permissions, and What Actually Executes

Symbol pi

a_t = \pi(c_t).

\pi

What this part means

pi is an input to the expression that computes the quantity on the left.

Its job in the formula

pi is an input to the expression that computes the quantity on the left.

Full expressionSymbol piArticle 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 function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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See this notation across published equations →

Sources cited in the article section

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