Equation 9 · Part 3 · Claude Code, From First Principles: The Agentic Loop, Permissions, and What Actually Executes

Symbol a_t

c_{t+1} = c_t \oplus (a_t,\ o_t).

a_t

What this part means

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

Its job in the formula

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

Full expressionSymbol a_tArticle meaning

The passage around this formula

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: $c_{t+1} = c_t \oplus (a_t,\ o_t)$ .…

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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.

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

See this notation across published equations →

Sources cited in the article section

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