Asymptotic Rigidity and Boundary Structure of Yang's Numerical Invariants for the Bidisk Submodules $[z^k-w^\ell]$

Let \[ M_{k,\ell}=[z^k-w^\ell]\subset H^2(\mathbb D^2), \qquad k,\ell\in\mathbb N,\quad k\ne\ell . \] We study the large-index asymptotics of Yang's numerical invariants and the boundary structure of their generating function. Starting from the exact staircase formula obtained in our preceding work,