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The exact change of variables from response thresholds to section parameters

theorem Papers.Rockel2026XiBlest.extremalQ_mem (b : ℝ) (hb : 0 < b) (v : ↑unitInterval) : extremalQ b hb v ∈ Set.Icc (-1 / b) 1

theorem Papers.Rockel2026XiBlest.extremalQ_normalizationMean (b q : ℝ) (hb : 0 < b) (hq : q ∈ Set.Icc (-1 / b) 1) : extremalQ b hb ⟨normalizationMean b q, ⋯⟩ = q

theorem Papers.Rockel2026XiBlest.normalization_substitution (b : ℝ) (hb : 0 < b) (G : ℝ → ℝ) (hG : Continuous G) : ∫ (v : ↑unitInterval), G (extremalQ b hb v) = ∫ (q : ℝ) in -1 / b..1, G q * -deriv (normalizationMean b) q