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Equation 20 · Part 2 · OpenAI Codex as a Software-Engineering System: Models, Harnesses, and Evidence

Symbol f

hk+1=f(hk,ok,ak)h_{k+1}=f(h_k,o_k,a_k)
ff

What this part means

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

Its job in the formula

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

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 hk+1h_{k+1}=f(hkh_k,oko_k,aka_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.

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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See this notation across published equations →

Sources cited in the article section

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