Equation 1 · Part 6 · Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex

Symbol a_T-1

\tau=(s_0,o_0,a_0,s_1,\ldots,a_{T-1},s_T),

a_{T-1}

What this part means

$a_T$ -1 is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

$a_T$ -1 is one of the signed contributions combined to compute the quantity on the left.

Full expressionSymbol a_T-1Article meaning

The passage around this formula

Let a task generate a trajectory $\tau=(s_0,o_0,a_0,s_1,\ldots,a_{T-1},s_T)$ . where $s_t$ is environmental state, $o_t$ the agent’s observation, and $a_t$ its action. Task success is not a property of the final message. It is an externally evaluated predicate V( $s_T$ ,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.

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Sources cited in the article section

[2] Introducing GPT-5.3-Codex ↗

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