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The phrase "asserted that given" is correct and usable in written English.
It can be used when introducing a statement or claim that is based on certain conditions or assumptions.
Example: "The researcher asserted that given the current data, the hypothesis was valid."
Alternatives: "claimed that considering" or "stated that based on".
Exact(4)
Mr. Rehman asserted that given urgent efforts by the Americans to start negotiations with the Taliban in Afghanistan, American weapons transported through NATO supply lines could ultimately be turned back on Pakistan, earning loud applause from fellow lawmakers.
Ayatollah Muhammad Husayn Fadlallah, the Lebanese cleric whose spiritual authority is recognized by Hezbollah, gave an interview to the Beirut newspaper Al Safir in which he asserted that given their impermissible choice of targets, the 9/11 bombers were not martyrs but "merely suicides".
Some have asserted that, given the expertise of technology companies, they should be able to construct a system that keeps the data of nearly all users secure but still allows the data of very few users to be read covertly when a proper warrant is served.
However, it is asserted that, given the methodological difficulties of evaluating health professionals' performance and the educational impact of interventions, descriptive and observational studies can still provide valuable information [ 7].
Similar(56)
It asserts
But critics assert that given its partial ownership by airlines that supply three-quarters of all domestic air travel, Orbitz could allow its participating airlines to set anti-competitive fare structures.
In this respect, Pilling et al. [5] were correct to assert that given that formal analysis of their data "would lack the power to detect anything other than very large treatment effects", a formal analysis "would be potentially misleading".
A stronger version makes an in principle claim about our human capacities and thus asserts that given our human cognitive limits we will never be able to bridge the gap.
The organization asserts that given what we know about the link between climate change and children's health, "failure to take prompt, substantive action would be an act of injustice to all children".
As the press release asserts, that gives riders less than a week to "sample and become acclimated to new travel options".
Critics asserted that giving a writing award to a pop music figure undercut the value of the honor.
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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