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A sharp local threshold is identified, stability under bounded perturbations is proved, monotonicity in $k$ is established, and an intrinsic $\Theta(\log n)$ separation between local and global realizability is shown.
This work develops a geometric framework for analyzing the robustness of neighborhood-based fairness audits under bounded perturbations, establishes sufficient conditions for neighborhood invariance, quantifies how neighborhood replacement propagates to audit instability, and introduces audit volatility, a measure of t...
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