Equation 1 · OpenAI Codex as a Software-Engineering System: Models, Harnesses, and Evidence
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 C_t
is part of the quantity the equation computes from the expression on the right.
=
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
A useful abstraction is . where is the model policy at time t ; is the harness and its context/state machinery; is the available tool set; is the permission and sandbox policy; is the execution environment; is the collection of verification functions; and represents user and institutional authority. The time index is essential. OpenAI can update the model, CLI, documentation, or cloud runtime without changing the product name.
Sources cited in the article section
These citations give research context. Read each source to check which claims it supports.
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