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Equation 3 · Part 1 · Ten Failure Modes That Define Production AI Agent Architectures

Symbol r

r(n)=c n.r(n) = c^{\,n}.
rr

What this part means

r is part of the quantity the equation computes from the expression on the right.

Its job in the formula

r is part of the quantity the equation computes from the expression on the right.

The passage around this formula

A simplified model makes the handoff-chain version of this concrete. Suppose each handoff in a sequential chain of agents preserves only a fraction c ∈\in (0,1) of the decision-relevant context generated before it — the rest summarized away, dropped, or simply never passed, as when a subagent returns only a final message rather than its working trace. After n sequential handoffs, the fraction of the original context still available at the far end of the chain is r(n)=c nr(n) = c^{\,n}. The decay is geometric, not linear: at c = 0.8 , five hops in sequence leave roughly a third of the original context standing, and ten hops leave roughly a tenth. This is a deliberately crude model — real handoffs…

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the article section

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