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The phrase "ascertain this assertion" is correct and usable in written English.
It can be used when you want to confirm or verify a statement or claim made by someone.
Example: "Before we proceed with the project, we need to ascertain this assertion about the budget constraints."
Alternatives: "verify this claim" or "confirm this statement".
Exact(1)
This is however hampered by the lack of direct evidence to conclusively ascertain this assertion.
Similar(59)
To ascertain this, we conducted three sets of experiments.
The present work was undertaken to ascertain this relationship.
Unfortunately, we have been unable to ascertain this.
We shall consider two different cases to ascertain the preceding assertion.
The moderators checked repeatedly with participants to ascertain assertions and meanings.
This assertion is logically true, and to ascertain the possibility one needs to stratify the population according to blood glucose level, genotype the participants, and survey TEI under an ad lib diet.
See [ 30] for a controversial discussion of this assertion.
"We have not ascertained whether the assertions are true," he told the Windy City Times in the interview.
This assertion is baseless.
hearing this assertion, Knight rolled his eyes.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com