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Prove KMedianThreshold (openai/math family 125: The approximation threshold for metric $k$-median) in Lean 4…

Prove KMedianThreshold (openai/math family 125: The approximation threshold for metric $k$-median) in Lean 4…: a task in openai/math as Harbor environments (Harbor dataset). Context: this statement belongs to family 125 of the release, The approximation threshold for metric $k$-median (Theoretical…

The task

Context: this statement belongs to family 125 of the release, *The approximation threshold for metric $k$-median* (Theoretical computer science). The family as a whole: Gives a deterministic polynomial-time $(1+2/e+\varepsilon)$-approximation for finite rational metric $k$-median with specified candidate facilities,…

Part of raising-heart/openai-math.