Function pick_sigma 

pub fn pick_sigma(
    sigma_min: Number,
    sigma_max: Number,
    mu_min: Number,
    mu_max: Number,
    avrg_compl: Number,
    sigma_tol: Number,
    qf_tol: Number,
    max_steps: i32,
    q: impl FnMut(Number) -> Number,
) -> Number

Sigma-bracket selection + golden-section orchestrator. Mirrors IpQualityFunctionMuOracle.cpp::CalculateMu lines 329-385.

q is a black-box q(σ) evaluator (typically constructed by composing the affine + σ·centering step into a trial point and calling evaluate_quality_function).

Returns the σ that approximately minimizes q on the picked bracket; the caller then sets μ_new = σ · avrg_compl and clamps to [mu_min, mu_max].