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Equation 20 · Part 8 · OpenAI Codex as a Software-Engineering System: Models, Harnesses, and Evidence

subscript

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

What this part means

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.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

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

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Sources cited in the article section

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