  We propose a new theory framework to study the isospin-symmetry breaking
correction $\delta_\text{C}$ in superallowed nuclear beta decays, crucial for
the precise determination of $|V_{ud}|$. Based on a general assumptions of the
isovector dominance in ISB interactions, we construct a set of functions
$F_{T_z}$ which involve nuclear matrix elements of isovector monopole operators
and the nuclear Green's function. Via the functions $F_{T_z}$, a connection of
$\delta_\text{C}$ to measurable electroweak nuclear radii is established,
providing an experimental gauge of the theory accuracy of $\delta_\text{C}$. We
outline a strategy to perform ab-initio calculations of $F_{T_z}$ based on the
Lanczos algorithm, and discuss its similarity with other
nuclear-structure-dependent inputs in nuclear beta decays.
