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Equation 1 · Part 10 · Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex

subscript

τ=(s0,o0,a0,s1,…,aT−1,sT),\tau=(s_0,o_0,a_0,s_1,\ldots,a_{T-1},s_T),
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

Let a task generate a trajectory τ=(s0,o0,a0,s1,…,aT−1,sT)\tau=(s_0,o_0,a_0,s_1,\ldots,a_{T-1},s_T). where sts_t is environmental state, oto_t the agent’s observation, and ata_t its action. Task success is not a property of the final message. It is an externally evaluated predicate V(sTs_T,g) over final state and goal g . System reliability under task distribution D is

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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.

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

Sources cited in the article section

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