Suppose $kappa$ is an inaccessible cardinal. Let $G instances H$ be $mathrm{Col}(omega_1,{<}kappa) instances mathrm{Add}(omega,kappa)$-generic over $V$. Let $X subseteq kappa$ be $mathrm{Add}(kappa,1)$-generic over $V[G][H]$. Since $X$ codes each bounded subset of $kappa$ as an interval-subsequence, $V[X] fashions kappa = omega_2 = 2^omega$. Does there exist an internal mannequin of $V[X]$ with the identical cardinals satisfying CH?

Be aware: By arguments much like these of Part 2.1 right here, $G notin V[H][X]$.