Equation 21 · 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 mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. 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 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.
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 this expression with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
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.
Return to Ten Failure Modes in Agentic Coding, from Prompt Injection to False Completion