Equation 9 · Part 4 · Claude Code, From First Principles: The Agentic Loop, Permissions, and What Actually Executes

Symbol o_t

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

o_t

What this part means

the producing an observation.

Its job in the formula

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

Full expressionSymbol o_tArticle meaning

Where the article explains it

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.

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: $c_{t+1} = c_t \oplus (a_t,\ o_t)$ . The loop repeats until $\pi$ emits a stop rather than a tool call. Nothing in this is exotic; it is the standard shape of a tool-using agent.…

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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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