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Published equation contexts

diLi>Ki+Fid_i L_i > K_i+F_i

Why this formula appears here

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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LiL_i

Symbol L_i

LiL_i is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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Published contexts (1)

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

Equation 44 · AI Agents & Systems

Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex

This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.

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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