Equation 12 · Claude Code, From First Principles: The Agentic Loop, Permissions, and What Actually Executes
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
the producing an observation. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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subscript
subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
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What the article says around this equation
The loop repeats until 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: is not a hypothetical action but a call to a real interpreter with real side effects on a real machine, is not simulated feedback but the actual return value of that call, and the boundary between “the model decided” and “the harness allowed” is enforced by software, not by the model’s own restraint.
Sources cited in the article section
- [2] How Claude Code works ↗
- [11] Dive into Claude Code: The Design Space of Today's and Future AI Agent Systems ↗
These citations give research context. Read each source to check which claims it supports.