Equation 9 · Part 5 · Claude Code, From First Principles: The Agentic Loop, Permissions, and What Actually Executes

=

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

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

Full expression=Article 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: $c_{t+1} = c_t \oplus (a_t,\ o_t)$ . 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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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

Open the illustrated equality: what the equals sign claims guide →

Sources cited in the article section

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