Symbol r
r is part of the quantity the equation computes from the expression on the right.
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Why this formula appears here
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 (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 . 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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Symbol n
n is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.
Read this term in its guide →Symbol c^n
is an input to the expression that computes the quantity on the left.
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Equation 3 · AI Agents & Systems
Ten Failure Modes That Define Production AI Agent Architectures
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.
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 (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 . 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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