Equation 20 · Ten Failure Modes in Agentic Coding, from Prompt Injection to False Completion
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
Read it piece by piece
Symbol K_i
is part of the quantity the equation computes from the expression on the right.
Symbol p_i
effective prevention, detection, containment, and recovery probabilities under a simplified independence assumption.
Symbol d_i
effective prevention, detection, containment, and recovery probabilities under a simplified independence assumption.
Symbol c_i
effective prevention, detection, containment, and recovery probabilities under a simplified independence assumption.
Symbol r_i
effective prevention, detection, containment, and recovery probabilities under a simplified independence assumption.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →subscript
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.
How to interpret it
Read it with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
For failure mode i , define control coverage . where ,,, are effective prevention, detection, containment, and recovery probabilities under a simplified independence assumption. The equation should not be used to manufacture precise risk numbers; controls are correlated and measurements sparse. It communicates why a single impressive guardrail cannot justify broad authority.
For background, read the article’s source list.
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