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Exact xi and correlation ratio of the folded-uniform model

theorem Verification.foldKernel_square_integral (v : ↑unitInterval) : ∫ (u : ↑unitInterval), foldKernel v u ^ 2 = (unitClamp (2 * ↑v) + 3 * unitClamp (2 * ↑v - 1)) / 4

theorem Verification.foldedUniform_xi : foldedUniform.chatterjeeXi = 1 / 4

theorem Verification.foldKernel_response_integral (u : ↑unitInterval) : ∫ (v : ↑unitInterval), foldKernel v u = 1 / 2

theorem Verification.foldedUniform_conditionalMean : conditionalMean foldedUniform =ᵐ[MeasureTheory.volume] fun (x : ↑unitInterval) => 1 / 2

theorem Verification.foldedUniform_correlationRatio : correlationRatio foldedUniform = 0