Equation 2 · Ten Failure Modes That Define Production Tool-Protocol Integrations
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properties of the workload and the network. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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The shape of the exposure is simple enough to write down. Let n be the number of side-effecting tool calls in a session, p the probability that any one call’s response is lost after the server has already executed it, and i the fraction of those calls actually covered by a working, executor-enforced idempotency key. Then the expected count of uncontrolled duplicate side effects across the session is approximately
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