An Exact Apéry Limit for the AESZ 182 Calabi–Yau Recurrence

We prove the 2008 Almkvist–van Straten–Zudilin conjecture for the Apéry limit of the Calabi–Yau recurrence AESZ #182:

lim_{n→∞} b_n/a_n = (3/11)ζ(3).

The proof gives a determinant Laurent-period realization, constructs a relative cap whose projected normal function satisfies an inhomogeneous Picard–Fuchs equation, and combines exact subdominance with the D’Andrea–Lalín determinant Mahler measure. We also prove

a_n ~ (9/(2π²)) · 27^n/n².

The source package and exact verification scripts are included.