这位研究者提出的理论在科学审查下站不住脚。

The theory proposed by the researcher ___doesn't ___hold ___water under scientific scrutiny.

我们必须证明他们的主张夸大其词且站不住脚。

We must demonstrate that their claims are exaggerated and ___don't ___hold ___water.

他对犯罪当晚的不在场证明在警方看来站不住脚。

His alibi for the night of the crime ___doesn't ___hold ___water with the police.