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Proposition 3(ix): classical concordance of the signed tent family

theorem Papers.OrendayLaresRockel2026XiBeta.integral_tentDisplacement (b : ℝ) (hb : b ∈ Set.Icc (-1) 1) : ∫ (v : ↑unitInterval), (tentDisplacement b hb).toFun v = b * |b| / 4

theorem Papers.OrendayLaresRockel2026XiBeta.leftBoundary_rho (b : ℝ) (hb : b ∈ Set.Icc (-1) 1) : (leftBoundary b hb).spearmanRho = 3 / 4 * b * |b|

theorem Papers.OrendayLaresRockel2026XiBeta.leftBoundary_tau (b : ℝ) (hb : b ∈ Set.Icc (-1) 1) : (leftBoundary b hb).kendallTau = 1 / 2 * b * |b|