We perform an ab initio quantum Monte Carlo calculation of the isospin-symmetry-breaking correction ${\delta }_C$ to the superallowed $\beta$ decay of ${}^{10}\mathrm{C}$. Using both phenomenological and chiral nuclear interactions, we evaluate the Fermi matrix element and quantify its deviation from the canonical $\sqrt{2}$ value. The resulting ${\delta }_C$ values lie in the range $\approx 0.15–0.25\%$ and are consistent, within sizable uncertainties (approximately $34\%–65\%$ relative), across Hamiltonians, indicating no statistically significant dependence on the choice of nuclear interaction. The extracted values of $V_{\text{ud}}$ are also found to be compatible with current determinations within these uncertainties.

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• Beta decay
• Nuclear structure & decays
• 6 ≤ A ≤ 19
• Ab initio calculations
• Monte Carlo methods