Equation 20 · Part 5 · OpenAI Codex as a Software-Engineering System: Models, Harnesses, and Evidence

Symbol a_k

h_{k+1}=f(h_k,o_k,a_k)

a_k

What this part means

$a_k$ is an input to the expression that computes the quantity on the left.

Its job in the formula

$a_k$ is an input to the expression that computes the quantity on the left.

Full expressionSymbol a_kArticle meaning

The passage around this formula

Long sessions pose a lossy-state problem. When a transcript exceeds context capacity, a harness may compact earlier interaction into a summary. If $h_{k+1}$ =f( $h_k$ , $o_k$ , $a_k$ ) compresses state, reliability depends on whether f preserves commitments, failed hypotheses, file identities, and unresolved constraints. More context tokens do not remove this requirement; they postpone it.

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.