0-GAS and point-wise ULIM imply ISS for time-delay systems

Consider the time-delay system on $\mathcal X^n$ with inputs in $\mathcal U^m$. 0-GAS plus point-wise ULIM conjecture. If the system is 0-GAS and satisfies the point-wise version of the ULIM property described immediately before the claim, then it is ISS. This would resolve the gap between point-wise visits of the state to an input-dependent neighborhood and the history-wise ULIM property used in known ISS characterizations; its resolution is not supplied.