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Equation 44 · Part 5 · Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex

addition

diLi>Ki+Fi.d_i L_i > K_i+F_i.
addition

What this part means

Add the term after the plus sign to the term or group before it.

Its job in the formula

Add the term after the plus sign to the term or group before it.

The passage around this formula

Checkpoint placement is a value-of-information problem. Let an unchecked latent error at stage i create expected downstream loss LiL_i , a check cost KiK_i , detection probability did_i , and false-alarm cost FiF_i . A check is favorable when, approximately, diLi>Ki+Fid_i L_i > K_i+F_i. High-value checkpoints occur before expensive or irreversible transitions: after specification, before schema migration, after dependency changes, before broad refactors, before network or credential escalation, and before merge or deployment. Cheap deterministic checks should run earlier and more often than expensive human review.

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Learn the underlying idea

Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

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