Equation 6 · Part 3 · Claude Code, From First Principles: The Agentic Loop, Permissions, and What Actually Executes

Symbol c_t

a_t = \pi(c_t).

c_t

What this part means

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

Its job in the formula

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

Full expressionSymbol c_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:

Read this part in the article →

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.

Open the illustrated subscripts: which member of a family? guide →

See this notation across published equations →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.