← All parts of this equation

Equation 1 · Part 8 · Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex

=

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

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

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

Read this part in the article →

Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

Open the illustrated equality: what the equals sign claims guide →

Sources cited in the article section

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