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Equation 2 · Ten Failure Modes in Agentic Coding, from Prompt Injection to False Completion

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Risk⁡(a)=P(unsafe proposal)⋅P(authorization∣proposal)⋅P(escape detection)⋅L(a),\operatorname{Risk}(a)= P(\text{unsafe proposal}) \cdot P(\text{authorization}\mid\text{proposal}) \cdot P(\text{escape detection}) \cdot L(a),

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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.

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aa

Symbol a

the risk of an action.

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PP

Symbol P

P is one factor in the product that computes the quantity on the left.

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LL

Symbol L

consequence.

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=

=

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

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multiplication

multiplication

Multiply the quantities on either side.

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What the article says around this equation

The risk of an action a is not reducible to model error probability. A simple decomposition is Risk⁡(a)=P(unsafe proposal)⋅P(authorization∣proposal)⋅P(escape detection)⋅L(a)\operatorname{Risk}(a)= P(\text{unsafe proposal}) \cdot P(\text{authorization}\mid\text{proposal}) \cdot P(\text{escape detection}) \cdot L(a). where L(a) is consequence. Better models can reduce the first factor. Sandboxes, permission policy, independent evaluators, and staged execution reduce the others. Security architecture should assume every factor is nonzero.

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