Fixed-scale shift growth, with the constant chosen before varying data.

theorem MathlibNt.AnalyticNumberTheory.LargeSieve.LiLiuPrereqFouvry.directPayKSecondary_tau {δ : ℝ} (hδ : 0 < δ) : ∃ (Ca : ℝ), 0 < Ca ∧ ∀ (Cscale : ℝ), 1 ≤ Cscale → ∀ (x : ℝ), 1 ≤ x → ∀ (a : ℤ), |↑a| ≤ Cscale * x → ↑a.natAbs.divisors.card ≤ Ca * Cscale ^ δ * x ^ δ

The divisor constant depends only on delta; the scale loss is explicit.