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The exact attainable region (Theorem 1)

Both endpoints are constructed explicitly. Fixed-beta mixtures attain every intermediate xi, so the existential conclusion has no supplied boundary hypotheses.

theorem Papers.OrendayLaresRockel2026XiBeta.exact_xi_beta_region (x b : ℝ) : (∃ (C : ProbabilityTheory.Copula 2), C.chatterjeeXi = x ∧ C.blomqvistBeta = b) ↔ x ∈ Set.Icc 0 1 ∧ b ∈ Set.Icc (-1) 1 ∧ |b| ^ 3 ≤ 2 * x

The set equality in Theorem 1, stated as membership equivalence.