Equation 6 · 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.
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol a_t
is part of the quantity the equation computes from the expression on the right.
Symbol pi
pi is an input to the expression that computes the quantity on the left.
Symbol c_t
is an input to the expression that computes the quantity on the left.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →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.
How to interpret it
Read it with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
Let be the context available to the model at step t : system instructions, conversation so far, file contents, tool outputs. The model is a policy that, given , emits either a final answer or a tool call : . Claude Code executes — subject to a permission check described in the next section — against the real filesystem, shell, or network, producing an observation : a diff applied, a command’s stdout and exit code, a search result. That observation is appended to the context for the next step:
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.