← Back to article

Equation 14 · OpenAI Codex as a Software-Engineering System: Models, Harnesses, and Evidence

What does this equation mean?

ak∼πθ(a∣o≤k,g,hk).a_k \sim \pi_{\theta}(a\mid o_{\le k},g,h_k).

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 a bound: one expression must stay on the indicated side of the other 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.

Read it piece by piece

aka_k

Symbol a_k

aka_k is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Understand this part →

πθ\pi_{\theta}

Symbol pi_θ

pi_θ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Understand this part →

aa

Symbol a

a is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Understand this part →

o≤ko_{\le k}

Symbol o_ ≤ k

the model receives an observation history.

Understand this part →

gg

Symbol g

the task goal.

Understand this part →

hkh_k

Symbol h_k

the harness state.

Understand this part →

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.

Understand this part →

How to interpret it

Read this expression with the definitions, units, and assumptions supplied by the article.

What the article says around this equation

At an agent step k , a model receives an observation history o≤ko_{\le k} , task goal g , and harness state hkh_k , then proposes an action: ak∼πθ(a∣o≤k,g,hk)a_k \sim \pi_{\theta}(a\mid o_{\le k},g,h_k). The action might request a file read, search, patch, shell command, test, browser interaction, or delegation. It is not yet an environmental transition. The harness parses the proposal, checks that it matches an available tool schema, applies policy, executes permitted operations, and converts results into the next observation.

Read the equation in its article →

Sources cited in the article section

These citations give research context. Read each source to check which claims it supports.

Return to OpenAI Codex as a Software-Engineering System: Models, Harnesses, and Evidence

See this formula across 1 published context →

Browse the mathematical compendium →