← All parts of this equation

Equation 14 · Part 4 · OpenAI Codex as a Software-Engineering System: Models, Harnesses, and Evidence

Symbol o_ ≤ k

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

What this part means

the model receives an observation history.

Its job in the formula

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

Where the article explains it

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 passage around this formula

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 this part in the article →

Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

See this notation across published equations →

Sources cited in the article section

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