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The exact xi = 3/10 slice and both sharp gap signs

theorem Papers.AnsariRockel2026XiRho.abs_rho_sub_xi_le (C : ProbabilityTheory.Copula 2) : |C.spearmanRho| - C.chatterjeeXi ≤ 2 / 5

theorem Papers.AnsariRockel2026XiRho.abs_rho_sub_xi_eq_iff (C : ProbabilityTheory.Copula 2) : |C.spearmanRho| - C.chatterjeeXi = 2 / 5 ↔ C = unitDiagonalBand ∨ C = unitDiagonalBand.reflect {1}

theorem Papers.AnsariRockel2026XiRho.xi_three_tenths_slice (y : ℝ) : (∃ (C : ProbabilityTheory.Copula 2), C.chatterjeeXi = 3 / 10 ∧ C.spearmanRho = y) ↔ |y| ≤ 7 / 10

The complete horizontal slice of Theorem 1 at its maximal-gap point.

theorem Papers.AnsariRockel2026XiRho.xi_three_tenths_rho_max_eq_iff (C : ProbabilityTheory.Copula 2) (hx : C.chatterjeeXi = 3 / 10) : C.spearmanRho = 7 / 10 ↔ C = unitDiagonalBand

Uniqueness of the positive endpoint on this full slice.