Equation 10 · 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 A_g
is an input to the expression that computes the quantity on the left.
Symbol A_u
is an input to the expression that computes the quantity on the left.
Symbol g
g is an input to the expression that computes the quantity on the left.
Symbol s
s is an input to the expression that computes the quantity on the left.
=
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
Let user-intended authority be and agent-held authority be . The dangerous excess is . where intended authority depends on goal g and state s , not merely user identity.
Sources cited in the article section
These citations give research context. Read each source to check which claims it supports.
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