addition

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. What matters for this article is what each symbol is standing in for in a real, shipped product: $a_t$ is not a hypothetical action but a call to a real interpreter with real side effects on a real machine, $o_t$ is not simulated feedback but…

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