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Equation 16 · Reliable AI Agents Are Control Systems, Not Chatbots

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passk\mathrm{pass}^k

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This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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kk

Symbol k

k is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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superscript

superscript

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

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What the article says around this equation

The empirical warning appears in agent benchmarks. SWE-bench constructs software tasks from real GitHub issues and associated code changes, forcing systems to coordinate edits across repositories rather than complete isolated snippets [ 9 ] . Its scores are informative, but they remain conditional on a particular harness, task filtering, test infrastructure, and contamination controls. The τ\tau -bench work goes further by evaluating tool-using agents against domain rules and final database states. In its reported experiments, leading function-calling agents completed fewer than half of tasks, and consistency over repeated trials deteriorated sharply; the proposed passk\mathrm{pass}^k perspective…
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The empirical warning appears in agent benchmarks. SWE-bench constructs software tasks from real GitHub issues and associated code changes, forcing systems to coordinate edits across repositories rather than complete isolated snippets [ 9 ] . Its scores are informative, but they remain conditional on a particular harness, task filtering, test infrastructure, and contamination controls. The τ\tau -bench work goes further by evaluating tool-using agents against domain rules and final database states. In its reported experiments, leading function-calling agents completed fewer than half of tasks, and consistency over repeated trials deteriorated sharply; the proposed passk\mathrm{pass}^k perspective makes repeated reliability visible rather than celebrating a lucky run [ 10 ] .

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