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Equation 16 · Part 2 · Reliable AI Agents Are Control Systems, Not Chatbots

superscript

passk\mathrm{pass}^k
superscript

What this part means

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.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

The passage around this formula

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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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.